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  • Mathematics and Statistics  (101)
  • Wiley-Blackwell  (101)
  • Nature Publishing Group
  • Springer Nature
  • 1995-1999
  • 1985-1989  (66)
  • 1980-1984  (35)
  • 1975-1979
  • 1940-1944
  • 1988  (66)
  • 1984  (35)
  • 1940
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  • Wiley-Blackwell  (101)
  • Nature Publishing Group
  • Springer Nature
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  • 1995-1999
  • 1985-1989  (66)
  • 1980-1984  (35)
  • 1975-1979
  • 1940-1944
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  • 1
    Electronic Resource
    Electronic Resource
    Masthead (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100101
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  • 2
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    Explicity resolvable equations with functional non-linearities (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 477-485 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the non-linear evolution equation μdu/dt+Bu+n(u)L(u)=h, where n(u) is a functional, and introduce assumptions which allow its explicit solution. Several concrete applications of our procedure are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100411
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  • 3
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    Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 197-223 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper a thermomechanical model for the dynamics of structural phase transitions in the so-called ‘shape memory alloys’ is developed. These materials exhibit rather spectacular hysteresis phenomena. The resulting mathematical model consists of a coupled and highly non-linear system of partial differential equations reflecting the balance laws of linear momentum and energy. For an appropriate weak formulation the local-in-time existence of weak solutions is shown.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100302
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  • 4
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    Explicit formula for scalar non-linear conservation laws with boundary condition (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 265-287 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove an uniqueness and existence theorem for the entropy weak solution of non-linear hyperbolic conservation laws of the form \documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{\partial }{{\partial t}}u + \frac{\partial }{{\partial x}}f\left(u \right) = 0 $$\end{document}, with initial data and boundary condition. The scalar function u = u(x, t), x 〉 0, t 〉 0, is the unknown; the function f = f(u) is assumed to be strictly convex. We also study the weighted Burgers' equation: α ∊ ∝ \documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{\partial }{{\partial t}}\left({x^\alpha u} \right) + \frac{\partial }{{\partial x}}\left({x^\alpha \frac{{u^2 }}{2}} \right) = 0 $$\end{document}.We give an explicit formula, which generalizes a result of Lax. In particular, a free boundary problem for the flux f(u(.,.)) at the boundary is solved by introducing a variational inequality. The uniqueness result is obtained by extending a semigroup property due to Keyfitz.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100305
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  • 5
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    Masthead (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100401
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  • 6
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    Unilateral contact with adherence (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 367-381 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The dissipative adhesive properties of a viscoelastic solid are investigated. An approximate problem is considered and an existence theorem is proved. Numerical computations are presented.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100403
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  • 7
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    A dual method to the collocation method (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 439-445 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article we consider methods which are related to the collocation method by interchanging the test and the trial spaces. Error estimates are derived. As a by-product we obtain some extensions to the known convergence results for the collocation method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100408
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  • 8
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    A stability result for distributed parameter identification in bilinear systems (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 447-456 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we give a stability result for the problem of identifying distributed parameters (for instance, a conductivity matrix) in partial differential equations. The result is used to establish an error estimate for an algorithm to identify the parameter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100409
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  • 9
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    Time-periodic solutions of wave equations on ∝1 and ∝3 (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 457-475 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The classical Paiey-Wiener theorem and Hilbert space methods are used to show the existence of time-periodic solutions of the wave equation wtt-wrr+λw=h, 0 〈 r 〈 + ∞, which are radially symmetric and have exponential decay as r → + ∞. This problem is obtained when considering a one-dimensional or three-dimensional problem, and should be thought of as a linearization of a semilinear problem in which the associated linear operator has point spectrum (- ∞, λ). When λ ≤ 0 there is uniqueness, otherwise there is a non-trivial finite-dimensional null space. Estimates on w, wt, wr are obtained, which show that in either case there is a continuous correspondence h → w, where w is a uniquely characterized solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100410
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  • 10
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    Unique continuation for Schrödinger operators and for higher powers of the Laplacian (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 531-542 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the unique continuation property for Schrödinger operators and its application for proving the non-existence of positive eigenvalues (embedded in the continuous spectrum). We also use the estimate given by Jerison and Kenig9 to prove unique continuation for higher powers of the Laplace operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100504
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  • 11
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    The optimal stability estimate for some ill-posed Cauchy problems for a parabolic equation (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 575-583 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the non-characteristic Cauchy problem ut-a(x)uxx-b(x)ux-c(x)u = 0, x ∊ (0, l), t ∊ I, u(0, t) = ϕ(t), ux(0, t) = 0, t ∊ I, where I = ∝ or I = ∝+ and u(x, 0) = 0, x ∊ [0, l], in the case I = ∝+. Assuming an a priori bound for ‖u(l,.)‖L2, we derive the exact Hölder type dependence of on ‖u(x,.)‖L2 on ‖ϕ‖L2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100507
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  • 12
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    Uniqueness for structural phase transitions in shape memory alloys (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 145-151 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The non-linear coupled equations arising from alloy mechanism \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {u_{tt} - a\left({u_x,\theta } \right)u_{xx} - \mu u_{xxt} - b\left({u_x,\theta } \right)\theta _x = f\left({x,t} \right),} \\ {c\left({u_x,\theta } \right)\theta _t - k\theta _{xx} - \alpha k\theta _{xxt} - \mu u_{xt}^2 - d\left({u_x,\theta } \right)u_{xt} = \lambda \left({x,t} \right),} \\\end{array} $$\end{document} have two important features: a may take negative values and c may be degenerate.The local existence has been proved in Reference 1, but the uniqueness was open. In this paper the uniqueness is proved. For a discussion of the physical model and for the justifications of the detailed technical assumptions to be made, we refer to Reference 1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100204
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  • 13
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    The capillary contact angle, II: The inclined plane (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 165-196 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In an earlier paper an hypothesis on the nature of the forces resisting motion of a liquid drop on a support surface II was introduced and tested in the (rotationally symmetric) case for which ll is a horizontal plane. In the present work II is chosen as an inclined plane, so that rotational symmetry fails. The hypothesis leads to a formal series development; in a restricted case the result is verified by a perturbation analysis, which yields the identical series.The series predictions are compared with results of computer calculations. A consequence of the analysis is an estimate for a Bohd number B0, such that a further increase in B would result in the fluid penetrating the support surface; thus an absolute upper bound B0, for stability of the envisaged configuration is obtained.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670100206
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  • 14
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    Masthead (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060101
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  • 15
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    Solvability of an initial boundary value problem for the euler equations in twodimensional domain with corners (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 1-22 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The aim of this paper is to prove the existence and uniqueness of local solutions of some initial boundary value problems for the Euler equations of an incompressible fluid in a bounded domain Ω ⊂ R2 with corners. We consider two cases of a nonvanishing normal component of velocity on the boundary. In three-dimensional case such problems have been considered in papers [12], [13], [14]. Similar problems in domains without corners have been considered in [2]-[6], [11]. In this paper the relation between the maximal corner angle of the boundary and the smoothness of the solutions is shown. The paper consists of four sections. In section 1 two initial boundary value problems for the Euler equations are formulated. In section 2 the existence and uniqueness of solutions of the Laplace equation in twodimensional domain with corners for the Dirichlet and Neumann problems is proved in the Sobolev spaces. In sections 3 and 4 we prove the existence and uniqueness of solutions of problems formulated in section 1, using the method of successive approximations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060102
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  • 16
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    Faedo-galerkin approximations in equations of evolution (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 41-54 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the evolution equation u' = Au + Nu u(0) = φu is a function on a real interval [0, T] with values in a Hilbert space H, A is a linear operator in H generating a continuous semigroup eAt and N is a nonlinear operator in H.We show that 1Existence of the exact solution implies existence of the Faedo-Galerkin Approximations.2Existence of the Faedo-Galerkin Approximations implies existence of the exact solution.3Uniform convergence of the Faedo-Galerkin Approximations to the exact solution.The Paper consists of two parts. In the first five sections we require that A possesses a complete orthonormal system of eigenfunctions, in section 6 we drop this requirement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060104
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  • 17
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    Functional differential equations with certain monotonicity properties (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 97-103 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The present paper is concerned with the study of retarded differential equations in n-space, which satisfy some monotonicity properties. Sufficient conditions are given guaranteeing that solutions are contained in the probability (n - 1)-simplex. Existence and uniqueness of constant solutions are proved. It is also shown that every solution converges to a constant as t → ∞.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060108
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  • 18
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    On the transmission problem of the helmholtz equation for quadrantsHerrn Prof. Dr. K. Nickel zum 60. Geburtstag am 9. 2. 1984 gewidmet (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 129-157 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The plane transmission problem of the Helmholtz equation for quadrants is characterized by a one-dimensional singular integral equation, which refers to the Fourier transform of the normal derivative of the solution along the x-axis. It is derived by solving the transmission problem for the upper and the lower half-plane involving a Neumann condition at y = 0. This is done by a two-dimensional Laplace transform technique. The inverse Laplace transform with respect to the second cartesian coordinate and the restriction of this one to y = 0 then lead to the integral equation. Thereby the transmission conditions of the original problem at y = 0 have to be taken into account. The resulting integral equation is of generalized Wiener-Hopf-type. It is solved via the contraction theorem imposing restricting conditions on the wave numbers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060110
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  • 19
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    Bifurcation of periodic solutions for wave equations with scalar nonlinearities (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 206-214 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We treat wave equations with “scalar nonlinearities” and demonstrate the connection between the bifurcation theory of an associated system of Hammerstein integral equations and the existence of periodic solutions of the nonlinear wave equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060114
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  • 20
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    Weak solutions of the initial value problem for the unmodified non-linear vlasov equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 262-279 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of weak LL-solutions of the initial value problem for Vlasov's equation is proved under rather general assumptions. In the three-dimensional case the solutions exist on the entire time axis.
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    URL: http://dx.doi.org/10.1002/mma.1670060118
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  • 21
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    A generalized jacobi theta function (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 327-344 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The delta function initial condition solution v*(x,t;y) at x = y ≥ 0 of the generalized Feller equation is used to define a generalized Jacobi Theta function \documentclass{article}\pagestyle{empty}\begin{document}$ \Theta (x,t) = \upsilon *(x,t;0) + 2\sum\limits_{n = 1}^\infty {v*(x,t;y_n)} $\end{document} for a sufficiently rapidly increasing and unbounded positive sequence {yy}. It is shown that Θ(x,t) is analytic in each variable in certain regions of the complex x and t planes and that it is a solution of the generalized Feller equation. For those parameters for which this equation reduces to the heat equation, Θ(x,t) reduces to the third Jacobi Theta function.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670060120
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  • 22
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    Applications of convex analysis and comparison functionals to extremum principles (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 353-370 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In many areas of applied mathematics, the govering equations can be expressed as dual equations which are elements in two vector spaces where a given functional defined on a cartesian product space has zero gradients. If this functional has a global saddle structure then the variational principle can be replaced by dual extremum principles of the Noble and Sewell type. The purpose of the present paper is to investigate how comparison functional which have convex, concave or saddle structure can be used to generate upper and lower bounding principles and critical sequences. The methods are illustrated by applications to the periodic solutions of a non-linear differential equation and the Fredholm integral equation.
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    URL: http://dx.doi.org/10.1002/mma.1670060122
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  • 23
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    Continuous dependence on geometry for the backward heat equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 433-448 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we are concerned with the development of criteria for stabilizing inherently unstable initial-boundary value problems under small errors in the geometry of the underlying domain. We consider in particular the initial-boundary-value problem for the backward heat equation assuming that some error has been made in characterizing the geometry of the domain under consideration. It is shown that solutions which belong to an appropriately defined constraint set depend continuously in L2 on errors in the geometry.
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    URL: http://dx.doi.org/10.1002/mma.1670060126
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    Transmutation via the momentum plane (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 467-495 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Transmutation methods are developed for equations of the form x2 ϕ“ + x2(k2” - q̃(x)) ϕ = (v2 - (1/4)) ϕ, with v as spectral variable, which correspond to problems in quantum scattering theory at fixed energy k2 (here v ˜ l + (1/2) with l complex angular momentum). Spectral formulas for transmutation kernels are constructed and the machinery of transmutation theory developed by the author for spectral variable k is shown to have a version here. General Kontrorovič-Lebedev theorems are also proved.
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    URL: http://dx.doi.org/10.1002/mma.1670060129
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    Two remarks on continuation procedures for solving some nonlinear equations (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 512-514 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let F be a mapping from Rn+1 into Rn, x(t) be a parametrization for ∣t - t0 ∣ 〈 c, of a smooth solution branch of the equation F(x) = 0, A(t) be the jacobian (n + 1) associated to a standard continuation method used for computing the solution branch. We study for a class of singularities at x(t0) the behaviour, near t = t0, of the determinant of A(t).
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    URL: http://dx.doi.org/10.1002/mma.1670060131
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    On the Vlasov-Fokker-Planck equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 527-538 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a modification of the Vlasov-Poisson equation, obtained by adding a diffusion term with respect to velocity. It describes, from a physical point of view, a plasma in thermal equilibrium, in a mean field limit situation. We find that the already known results concerning existence and uniqueness of the solutions for the ordinary Vlasov equation (constructive results and counterexamples) translate to our case.
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    URL: http://dx.doi.org/10.1002/mma.1670060134
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  • 27
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    Transport equations with boundary conditions of reverse reflection type (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 15-35 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A study is performed of transport equations on arbitrary three-dimensional domains with boundary conditions of reverse reflection type. The existence of the dominant eigenvalue of the criticality problem is proved and its independence of the functional setting and its continuous dependence on a variety of data are established. The corresponding time-dependent problem is shown to be well-posed, also for a conservative boundary. The relationship between the criticality and the time-dependent problem is given explicitly.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670100103
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    Masthead (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100201
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    On the principles of limiting absorption and limit amplitude for a class of locally perturbed waveguides. Part 1: Time-independent theory (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 125-144 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Let Ω be a local perturbation of the n-dimensional domain Ω0 = Ropf;n - 1 × (0, π). In a previous paper8 we have introduced the notion of an admissible standing wave. We shall prove that the principle of limiting absorption holds for the Dirichlet problem of the reduced wave equation in Ω at ω ≥ 0 if Ω does not allow admissible standing waves with frequency ω. From Reference 8, this condition is satisfied for every ω ≥ 0 if Ω ≠ Ω0, and v·x′ ≤ 0 on δΩ, where x′ = (x1,…, xn - 1, 0) and v is the normal unit vector on δΩ pointing into the complement of Ω. In contrast to this, the principle of limiting absorption is violated in the case of the unperturbed domain Ω0 at the frequencies ω = 1,2,… if n ≤ 3. The second part of our investigation, which will appear in a subsequent paper, is devoted to the principle of limit amplitude.
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    On the construction of global weak solutions in the Kynch theory of sedimentation (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 245-264 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We construct global weak solutions to the different modes of sedimentation appearing in the theory of Kynch and show that, with constant initial concentration, only five modes of sedimentation exist. We also generalize the method of construction to the case of a monotonically decreasing initial concentration.
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    A mathematical study of a continuum-state cross-bridge model of muscle contraction (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 289-302 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In the framework of the sliding-filament theory of muscle contraction, we develop a model which describes physioiogical cross-bridge activity with a continuum of states, from those which are detached and refractory to those which are attached. The latter are kinetically more important.An analytical study of the non-linear partial differential equations of the mathematical model shows existence and uniqueness of the solution.
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    Singularities of the Laplacian at corners and edges of three-dimensional domains and their treatment with finite element methods (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 339-350 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Three-dimensional Poisson problems containing boundary singularities are treated. The forms of the solutions for certain problems of this type are derived, where the domains of the problems can be represented in terms either of spherical- or of cylindrical-polar co-ordinates. These singular forms are used to augment the basis of a standard piecewise polynomial Galerkin space, thus producing an augmented Galerkin technique which is suited to the context of a problem involving a singularity. Error estimates are derived.
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    Ein resonanzphänomen in der theorie akustischer und elektromagnetischer wellenHerrn Professor Karl Nickel zum 60. Geburtstag am 9. 2. 1984 gewidmet (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 104-128 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We discuss the asymptotic behaviour of acoustic and electromagnetic waves, generated by given time-harmonic exterior forces with frequency ω, in the unbounded region between the parallel planes X3 = 0 and X3 = 1, and show that the principle of limiting amplitude is violated if ω = πn(n = 1, 2,…). For these values of the frequency, forces with compact support can be chosen such that the amplitudes of the waves increase with a logarithmic rate as t → ∞.
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    Thin elastic and periodic plates (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 159-191 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: This paper is devoted to the study of a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small. In the three studied limits (e → 0 then ω → 0), (ω → 0 then e → 0) and lately (e and ω → 0 together) the three dimensional equation of elasticity are approached by the two dimensional general equations of a linear anisotropic plate, the stretching and bending being coupled. This study points out the importance of the ratio of the two small parameters, indeed the moduli occuring in the two dimensional equations are different in the three limits. In each case a convergence proof is carried out.
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    Bifurcation phenomena in a free boundary problem for a circulating flow with surface tension (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 215-233 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A free boundary problem for a flow around a circle is analyzed. We find and mathematically prove that bifurcations from the trivial flow actually take place. Golubitsky-Schaeffer theory, together with a formula concerning variations of domains, enables us to clarify the behaviors of the branches of nontrivial solutions.
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    Truncated random variables with application to random surfaces (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 248-261 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: There has been considerable interest in obtaining discrete results for random surfaces. Standard results have been published in journals of physics or engineering which have emphasised the applications. This paper gives a detailed background of the mathematical methods needed so that the central connection, namely truncated random variables, between these standard results can be understood. Distributions of discrete peak measures are obtained from the distributions of discrete profile measures of a random Gaussian surface by applying results for the distributions of truncated random variables. This enable the moments to be obtained from known results for the truncated distributions.
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    Non-linear boundary value problems for the annular membrane: New results on existence of positive solutionsDedicated to Professor Wolfgang Wendland on the occasion of his 50th anniversary (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 37-49 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The Föppl-Hencky theory of small finite deflections has been applied to the study of axisymmetric deformations of annular membranes by various authors. The mathematical problem of uniqueness of tensile solutions for the corresponding non-linear boundary value problems in the full range of physically meaningful boundary data was solved only recently.3, 4 In this paper, a new integral equation technique of solution is developed which yields the existence of tensile solutions for a parameter range of the boundary data where previous investigations on this matter had not been successful. It is shown that tensile solutions no longer exist, when sufficiently large positive radial displacements are prescribed at the inner edge of the annulus.
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    On a thermal stress problem for contacting half-spaces with inclusions of other material involving a new method for computing potentials and singular integrals (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 225-243 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper deals with a thermal stress problem for contacting half-spaces of different materials having an inclusion of other material. With the aid of the contact tensor of two half spaces the problem is reduced to singular integral equations. Some new theorems on potentials with the contact tensor are used. Finally, a potential of the double layer with the contact tensor in the kernel and a singular integral operator, being the direct value of the potential, are calculated. For this a Kupradze method is applied, interpreting this potential as a solution of a contact problem of elastostatics. Some numerical experiments are communicated.
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    On the stationary flows of viscous, incompressible and heat-conducting fluids (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 329-337 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We consider a boundary-value problem describing the motion of viscous, incompressible and heat-conducting fluids in a bounded domain in ∝3. We admit non-homogeneous boundary conditions, the appearance of exterior forces and heat sources.Our aim is to prove the existence of a solution of the problem in Sobolev spaces.
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    Inversion of the exponential X-ray transform. I: Analysis (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 561-574 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The exponential X-ray transform arises in single photon emission computed tomography and is defined on functions on ∝n by , where μ is a constant. Approximate inversion, and inversion formulae of filtered back-projection type are derived for this operator in all dimensions. In particular, explicit formulae are given for convolution kernels (filters) K corresponding to a general point spread function E that can be used to invert the exponential X-ray transform via a filtered back-projection algorithm. The results extend and refine work of Tretiak and Metz17.
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    Injection of ideal fluid from two slots into a stream (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 585-594 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A cold gas is injected from two slots into a stream of hot gas. In a simple model this leads to a three-phase two-free-boundary problem. We prove, using the variational theory of Alt, Caffarelli and Friedman, the existence of the classical solution.
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    On a weakly formulated exterior problem from linear hydrodynamics (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 595-608 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we investigate a certain exterior boundary value problem for the inhomogeneous Helmholtz equation. We give sufficient conditions for the unique solvability of a weak formulation of this problem and show an interior regularity result for all weak solutions. As a special case the incompresible, irrotational and stationary fluid flow around a totally immersed obstacle (submarine problem) is included.
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    The optimization of directivity and signal-to-noise ratio of an arbitrary antenna array (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 153-164 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The authors consider the optimization of the signal-to-noise ratio of an arbitrary cylindrical antenna array. Existence of an optimal solution and convergence of finite-dimensional approximations is shown. The necessary optimality conditions are used to compute optimal solutions for some numerical examples.
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    Masthead (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670100301
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    Global existence for the Vlasov-Poisson/Fokker-Planck equation in many dimensions, for small data (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 487-497 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A global existence result for the Cauchy problem of the Vlasov equation with a diffusive term is given. Smallness of the initial data is needed to show, via a ‘dispersive’ argument, the existence and nearness of the solution to the free one.
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    Initial boundary value problems in one-dimensional non-linear thermoelasticity (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 517-529 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The local existence of classical smooth solutions to the equations of homogeneous non-linear thermoelasticity in one space dimension is proved for the physically reasonable Dirichlet boundary conditions for both bounded and unbounded domains assuming smooth data.
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    On spline approximation for a class of integral equations. I: Galerkin and collocation methods with piecewise polynomials (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 543-559 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We consider the numerical solution of a class of one-dimensional non-compact integral equations by Galerkin and collocation methods and their iterated variants, using piecewise polynomials as basis functions. In particular, we obtain new results for the stability of the approximation methods, without any restriction on the norm of the integral operators. Furthermore, we extend results of Chandler and Graham4,6 concerning error estimates and superconvergence to a more general class of operators.
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    Forward speed motions of a submerged body. The cauchy problem (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 371-392 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We consider the linearized problem for the ideal fluid flow induced by the horizontal motion of a fully immersed body. The system of equations is made up of an elliptic problem (P) and an initialvalue problem (R) which are coupled by a pseudo-differential operator T.We define a regularized Cauchy problem (R∊) using the Yosida approximation of T; we give energy and wave resistance estimates and finally we obtain existence uniqueness and regularity of the weak solution of (R) by taking the limit when ∊ goes to zero.
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    Half- and finite-range completeness for the equation of transfer of polarized light (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 393-416 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: On neglecting reflection by the surface the existence and uniqueness are proved for the solution of the equation of transfer of polarized light in a homogeneous semi-infinite or finite plane-parallel medium. A general LL-space formulation, where 1 ≤ p 〈 ∞, is adopted. The analysis concerns a vector-valued convolution equation, which is an equivalent form of the equation of radiative transfer and is solved with the help of Wiener-Hopf factorization, Fredholm index and cone preservation methods. The results are also proved for the equations obtained from the full equation of transfer by means of Fourier expansion and symmetry relations.
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    Exact bounds for the radially symmetric shape of confined plasma in the unit circle (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 496-511 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The method of “cone iteration”; is used to obtain exact bounds for the solutions of a class of nonlinear operator equations. The general theory is applied to the problem of finding radially symmetric solutions of the plasma problem in the unit circle. Existence and uniqueness results are obtained at the same time. Some numerical examples demonstrate the method's high degree of accuracy.
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    Application of the Schwarz function to boundary problems for Laplace's equation (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 67-86 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: A method is described for studying analytic boundary problems for the Laplace equation in a simplyconnected domain D of the plane. The aim is ultimately to obtain solutions in closed form when D is bounded by a simple analytic curve C with Schwarz function G. The basis for the procedure is that a functional F of the incompletely known boundary Cauchy data determines the solution and is analytic in D, and that there exists a further integral relation between these data and the analytic function G. Elimination of the unknown data from the latter relation by using the former leads to an integral on C that relates F to prescribed data and which, in some cases, may be solved for F in D. Some necessary properties of G are derived; in particular, it is shown that C must be a circle if G is analytic in D except for a single, simple pole (Theorem 1), or if a certain integral that appears prominently in this work is analytic throughout D (Theorem 2). The Dirichlet problem is treated in some detail. If C is a circle, a representation for the solution is obtained that is equivalent to one given by P. J Davis, and to the Poisson integral. When G is meromorphic in D and C is not a circle, Theorem 2 implies that the Davis result is not applicable, and the problem is reduced to that of solving Schröder's functional equation. Integral equations for F are obtained when C is an ellipse and G is multivalued in D. Other linear boundary value problems that can be handled are noted. A class of non-linear Riemann-Hilbert problems is described and studied briefly. For all these problems, closed solutions have been obtained when C is a circle; it is not clear whether closed solutions for other forms of C can be found without the explicit use of conformal mapping techniques. Finally, some possible generalizations to different equations and more complicated geometries are mentioned.
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    Periodic motions of a string vibrating against a fixed point-mass obstacle: II (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 55-67 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: A string fixed at both ends A and B, can oscillate in a plane which there is a fixed point obstacle, placed in the middle of the line AB. The string is initially at rest with a prescribed shape, symmetric with respect to the normal mid-plane of the segment AB. Using results established before [9] we find new periodic motions.
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    Integral formulation for a steady-state transport process with general boundary conditions (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 68-83 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: A linear equation for a particle steady-state transport process in a homogeneous slab of finite thickness with boundary conditions of general type is derived. This equation differs from the well-known integral equation for no-reentry boundary conditions because of the presence of a per-turbance linear operator which describes the effect of the re-emission of the particles incident at the wall. The properties of the resulting operator are investigated. The dependence of the first positive eigenvalue on physical parameters is studies in detail. The results obtained are enough to discuss the existence of a critical strictly positive solution of the physical problems which motivated this research.
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    Scattering theory for diffraction gratings (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 158-158 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670060111
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    Évolution quasi-statique des milieux visco-plastiques de maxwell-norton (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 192-205 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we deal with the existence and unicity of a solution of the Maxwell-Norton quasi-static problem. Some fundamental results concerning the functional spaces are first recalled. Then, by an implicit scheme, we obtain a discretized problem which is well-posed. By monotonicity techniques, we finally prove the convergence of the discrete solutions to the solution of the initial problem.
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    An existence theorem for compressible viscous and heat conducting fluids (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 234-247 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider an initial-boundary value problem of a flow of a viscous and heat-conducting gas in a bounded domain D ⊂ R3. We assume that the boundary S of D consists of two disjoint surfaces S1 and S2 of class C2, and that the gas enters D through the surface S1 and leaves D through the surface S2.Our aim is to prove the existence (locally in time) of a solution of the problem in anisotropic Sobolev spaces.
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    URL: http://dx.doi.org/10.1002/mma.1670060116
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    L2-boundary integral equations for the robin problem (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 345-352 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study an integral equation method for the exterior Robin problem for the Helmholtz equation where the boundary condition is interpreted in the L2-sense. In particular, we derive a composite integral equation from Green's theorem which is uniquely solvable for all wave numbers.
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    URL: http://dx.doi.org/10.1002/mma.1670060121
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    Some applications of a galerkin-collocation method for boundary integral equations of the first kind (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 280-325 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Here we apply the boundary integral method to several plane interior and exterior boundary value problems from conformal mapping, elasticity and fluid dynamics. These are reduced to equivalent boundary integral equations on the boundary curve which are Fredholm integral equations of the first kind having kernels with logarithmic singularities and defining strongly elliptic pseudodifferential operators of order - 1 which provide certain coercivity properties. The boundary integral equations are approximated by Galerkin's method using B-splines on the boundary curve in connection with an appropriate numerical quadrature, which yields a modified collocation scheme. We present a complete asymptotic error analysis for the fully discretized numerical equations which is based on superapproximation results for Galerkin's method, on consistency estimates and stability properties in connection with the illposedness of the first kind equations in L2. We also present computational results of several numerical experiments revealing accuracy, efficiency and an amazing asymptotical agreement of the numerical with the theoretical errors. The method is used for computations of conformal mappings, exterior Stokes flows and slow viscous flows past elliptic obstacles.
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    Exact and chapman-enskog solutions for the carleman model (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 417-432 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Chapman-Enskog procedure is applied to the Carleman model of the Boltzmann equation. It has been proved that the Carleman equations possess a solution on the time interval on which a smooth solution of the fluid-like equation exists. The calculations have been performed up to the first order i.e., to the Navier-Stokes-like equation. It has been shown that in this case a difference between an exact solution and the Chapman-Enskog solution is of order ∊2. Extension of the results to higher orders is also possible. This gives a justification of the Chapman-Enskog procedure as an asymptotic expansion method.
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    On the geometric form of free boundaries satisfying a bernoulli condition (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 449-456 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the x-y plane, let Ω denote an annular domain bounded by the simple closed curves ⌜ and ⌜*, such that the capacity potential U in Ω satisfies ∣ ▽ U∣ = 1 on ⌜. Assuming ⌜* to be known, we obtain qualitative properties of ⌜. For example, the number of local maxima or minima of the y-co-ordinate relative to ⌜ cannot exceed the corresponding number for ⌜*.
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    An error analysis of the tau method for a class of singularly perturbed problems for differential equations (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 457-466 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: By using classical results of Poincaré and Birkhoff we discuss the existence and uniqueness of solution for a class of singularly perturbed problems for differential equations. The Tau method formulation of Ortiz [6] is applied to the construction of approximate solutions of these problems. Sharp error bounds are deduced.These error bounds are applied to the discussions of a model problem, a simple one-dimensional analogue of Navier-Stokes equation, which has been considered recently by several authors (see [2], [3], [8], [10]). Numerical results for this problem [8] show that the Tau method leads to more accurate approximations than specially designed finite difference or finite element schemes.
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    Numerical Computation of Waves at High Frequencies by an Iterated WKB-Method (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 520-526 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An integral operator is defined, which allows to solve the equation by Neumann series for sufficiently large k 〉 0. The kernel is constructed by a modification of the WKB-method. This kernel is so simple that the operator can be used effectively for numerical calculations. Numerical results are discussed.
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    Sturm-Liouville eigenvalue problems on networks (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 383-395 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The description of heat conduction on ramified wires, for instance, leads to a Sturm-Liouville eigenvalue problem on a network. It is shown that these problems are special canonical eigenvalue problems in the sense of Hölder, and therefore they can be investigated within the theory of S-Hermitian eigenvalue problems. In particular, Wielandt's expansion theorem can be applied in order to obtain eigenfunction expansions.
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    An evolution equation with non-local non-linearities: Existence, uniqueness and asymptotic behaviourPart of this paper was written while the author was at The University of Cologne partially supported by the DAAD. (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 407-425 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An evolution equation with non-linearities of non-local type is investigated. Under various hypotheses on the non-linearities global existence and uniqueness of solutions to initial value problems is shown. Moreover the asymptotic behaviour of the solutions is determined by topological dynamics methods.
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    A Hilbert space approach to maximum entropy reconstruction (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 397-406 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We examine here the problem of reconstructing an X-ray attenuation function from measurements of its integrals. The approach that is taken is to maximize the difference of the entropy and the residual error in meeting the measurements. The solution of this optimization problem is constrained by requiring that the solution lie in a certain weakly compact subset of L2, to be determined by physical information.We show that the constrained optimization problem is well-posed: there exists a unique solution (even when the measured data are inconsistent) and the solution depends continuously on the measurements. In the course of proving this, we show that the entropy functional is continuous on L2. We further demonstrate that the solution of the optimization problem for a special case, must be piecewise constant.
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    On the geometric form of Bernoulli configurations (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 1-14 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In References 4 and 5, the author studied the geometric form of the free boundary Γ of an annular domain Ω, characterized by the Bernoulli condition that |∇U|=1 on Γ, where U is the capacity potential in Ω. It was shown, for example, that Γ has at most as many ν-extrema (for a given direction ν) or inflection points as the other boundary component Γ* of Ω, which is assumed given. Our purpose here is to extend the results in References 4 and 5 (wherever possible) to multiply connected regions for which some boundary components are given and others are free boundaries characterized by the Bernoulli condition. We present both positive results and counterexamples.
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    Reduction of quasilinear elliptic equations in cylindrical domains with applications (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 51-66 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For certain types of semilinear partial differential equations in a cylindrical domain small bounded solutions are known to lie on a so-called centre manifold of finite dimension. In this paper we prove the result for quasilinear partial differential equations of elliptic and parabolic type.Possible applications include free surface waves and problems in non-linear elasticity. Here we investigate, pars pro toto, the stationary inviscid potential flow in a channel with a free surface and an obstacle at the bottom.
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    Scattering of elastic waves in a perturbed isotropic half space with a free boundary. The limiting absorption principle (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 87-124 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article we consider the self-adjoint operator governing the propagation of elastic waves in a perturbed isotropic half space with a free boundary condition. We prove the limiting absorption principle in appropriate Hilbert spaces for this operator. We also prove decreasing properties for the eigenfunctions associated with strictly positive eigenvalues of this operator.The proofs are based on the limiting absorption principle for the self-adjoint operator governing the propagation of elastic waves in a homogeneous isotropic half space with a free boundary and on the so called division theorem for it. Both perturbations of R+2 ={(x1, x2) ∊ R2; x2 〉 0} and R+2 = {(x1, x2, x3) ∊ R3; x3 〉 0} are considered.
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    An approximation method for a fokker-planck-vlasov equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 23-40 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A simplified Fokker-Planck equation of statistical plasma physics is mathematically investigated. For the Cauchy problem a constructive approximation method is introduced. This procedure yields a sequence (fn) of approximate densities, uniformly converging to the problem's global classical solution with linear convergence velocity.
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    Variational formulation of the roller contact problem (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 84-96 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We formulate the roller contact problem in terms of variational inequality with certain pseudodifferentional operator, and discuss a finite element technique for its numerical solution.
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    Two classes of explicit solutions of the carleman model (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 515-519 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For the Carleman model we show two classes of global explicit solutions.
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    Local validity of the boltzmann equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 539-549 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The validity of the Boltzmann equation is proved, locally in time, by showing that its solution is a limit of solutions of the BBGKY hierarchy.
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    The Sommerfeld half-plane problem revisited, IV: Variations on a theme of Carlson and Heins (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 303-328 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A plane wave is incident upon an infinite set of equally spaced, semi-infinite parallel and staggered plates. The boundary conditions on the plates alternate between the Dirichlet and Neumann ones. This problem is formulated as a pair of coupled Wiener-Hopf integral equations and solved by a method proposed by A. E. Heins in 1950. For the case of specular reflection, that is, a single reflected plane wave, the magnitudes of the reflection coefficient and the transmission coefficients are determined.
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    On non-stationary Navier-Stokes flows with vanishing viscosity associated with a variational inequality (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 351-366 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let g is a positive increasing function with 1≤g(0). The existence of a unique solution of the Navier-Stokes flow associated with Kε,γ and the convergence of the solution to that of the Euler equations as the viscosity goes to zero are established.
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    Boundary value problems for static Maxwell's equations (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 427-437 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A generalized version of magnetostatics in differentiable manifolds is formulated. Different boundary value problems are treated as different representations of the same object as graphs of self-adjoint mappings. The Hodge theorem for a domain with the local segment property is proved.
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    Masthead (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    On the radius continuity of the models of polytropic gas spheres which correspond to the positive solutions of the generalized Emden-Fowler equation (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 499-516 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We completely answer the question which positive solutions of the Emden-Fowler equation , n 〉 ½, m 〉 - 1, m+n 〉 0 induce models of polytropic gas spheres of finite radius or finite mass. We continue and complete the investigation of the radius continuity of these models initiated by van den Broek and Verhulst8 in connection with a numerical analysis by Hénon7.
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    Masthead (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988) 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Superconvergence of the gradient for quadratic triangular finite elements (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 15-32 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    An extension of the one-dimensional von Rosenberg finite difference scheme to multidimensional problems of the convection dispersion equation (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 1-13 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Crank Nicolson implicit form of the finite difference analogue of the convection-dispersion equation does not yield stable solutions when the dispersion coefficient of the medium D is too small compared with the injected fluid velocity V - i.e, 0 〈 (R = 2D/V ΔX) 〈 1. Von Rosenberg developed a simple, highly accurate and stable finite difference scheme for the one-dimensional case of constant velocity and dispersion coefficient for 0 〈 R 〈 1. El-Ageli extended von Rosenberg's method to the multilayered case of varying velocity and dispersion coefficient. This paper goes a step further and extends von Rosenberg's scheme to the linear multidimensional system with constant velocities and dispersion coeffcients when: 0 〈 (Rx, Ry,…,) 〈 1. When this new scheme is compared with the conventional Crank-Nicolson method, it is found that even though there are some restrictions to the spacial grid spacings in relation to the time step, the computational effort is much less and the results obtained are stable.
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    On a moving boundary problem of transitional ballistics (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 69-90 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A hybrid algorithm for calculating the flow around a flat-nosed projectile moving through a fluid is established. At cells of fixed volume away from the projectile, Harten's total variation diminishing (TVD), second-order accurate, shock capturing scheme is utilized. Due to projectile motion, cells adjacent to the projectile can be treated as compressing or expanding in volume. For such cells, a local finite volume approach has been employed to derive a cell update algorithm.Proof of concept for the expanding cell scheme is established through calculating the one-dimensional flow behind a moving piston, whose theoretical solution is well-known. The resulting hybrid scheme is applied to the problem of blast wave simulation in axisymmetric geometries. Flow around a vertical muzzle brake is calculated for the case of an embedded moving projectile.
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    An explicit finite difference scheme based on the modified method of characteristics for solving convection-diffusion problems in one space dimension (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 119-138 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Finite differences are combined with the modified method of characteristics to develop an explicit scheme for solving convection-dominated convection-diffusion problems in one spatial dimension. Error analysis shows that the new algorithm is stable under a mild stability criterion. Problems with known analytical solutions are used to test the algorithm and demonstrate its convergence. Numerical solutions are free of numerical dispersion, undershoot and overshoot. The algorithm is easy to implement and requires small computational times for the test problems considered.
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    A regularization-stabilization technique for nonlinear conservation equation computations (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 165-171 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A regularization procedure for nonlinear conservation equations is introduced and demonstrated to have a stabilizing effect on the numerical solution of the associated approximate problem. Representative results for a least-squares finite-element method are given, and the numerical performance of the stabilization procedure explored. The effect of the regularization term is similar to a local numerical dissipation dependent on the numerical itegration time step.
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    The performance of numerical methods for elliptic problems with mixed boundary conditions (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 347-361 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider solving linear, second order, elliptic partial differential equations with boundary conditions of types Dirichlet (DIR), mixed (MIX), and nearly Neumann (Neu) by using software modules that implement five numerical methods (one finite element and four finite differences). They represent both the new generation of improved methods and the traditional ones; they are: Hermite collocation plus band Gauss elimination (HC), ordinary finite differences plus band Gauss elimination (5P), ordinary finite differences with Dyaknov iteration (DY), DY with Richardson extrapolation to achieve fourth order convergence (D4), and ordinary finite differences with multigrid iteration (MG). We carry out a performance evaluation in which we measure the grid size and the computer time needed to achieve three significant digits of accuracy in the solution. We compute the changes in these two measures as we change boundary condition types from DIR to MIX and MIX to NEU and then test the following hypotheses: (i) the performance of all the modules is degraded by introducing the derivative terms into the boundary conditions; (ii) finite element collocation (HC) is least affected; (iii) the fourth order modules (HC and D4) are less affected than the other second order modules; and (iv) the traditional 5-point finite differences (5P) are most affected. We establish these hypotheses with high levels of confidence by using several sample problems. The most significant conclusion is that a high order collocation method is preferred for problems with general operators and derivatives in the boundary conditions. We also establish with considerable confidence that these modules have the following rankings in absolute comparative time performance: MG (best), HC and D4, DY, and 5P (worst).
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690040407
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    A penalty finite element model for axisymmetric flows of non-Newtonian fluids (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 33-56 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690040104
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    On the finite element approximation of incompressible flows of an electrically conducting fluidThis work was performed under the auspices of the U. S. Department of Energy and under Grant AF-AFOSR-84-0131 while the author was in residence at the University of Pittsburgh. (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 57-68 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the finite element approximation of incompressible flows field of an electrically conducing fluid in the presence of a magnetic where it is assumed that this field is prescribed. A weak form is chosen that is similar in some respects to a weak form used by many authors for the Navier-Stokes equations. Existence and uniqueness results are presented for the weak problem. A finite element Algorithm is given for the approximate solution of the weak problem and error estimates are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690040105
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    Masthead (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988) 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690040201
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    Optimization of computational grids (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 95-117 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the problem of mesh grading or gridr-point redistribution using optimization techniques. Some representate forms of the objective functions are considered and the assocated scaling parameterization and nonlinear programming algorithms examined. Numerical results for representative test problems involving two-and three-dimensional grids are presented.
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    URL: http://dx.doi.org/10.1002/num.1690040202
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    Masthead (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988) 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690040301
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    Numerical comparison of preconditionings for large sparse finite element problems (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 139-157 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A numerical study of the efficiency of the modified conjugate gradients (MCG) is performed using different preconditioning schemes. The MCG behavior is evaluated in connection with the solution of large linear sets of symmetric positive definite (p.d.) equations, arising from the finite element (f.e.) integration of partial differential equations of parabolic and elliptic type and the analysis of the leftmost eingenspectrum of the corresponding matrices. A simple incomplete Cholesky factorization ICCG(O) having the same sparsity pattern as the original problem is compared with a more complex technique ICAJ (Ψ) where the triangular factor is allowed to progressively fill in depending on a rejection parameter Ψ. The performance of the preconditioning algorithms is explored on finite element equations whose size N ranges between 150 and 2300. The results show that an optimal Ψopt may be found which minimizes the overall CPU time for the solution of both the linear system and the eigenproblem. The comparison indicates that ICAJ (Ψopt) is not significantly more efficient than ICCG(O), which therefore appears to be a simple, robust, and reliable method for the preconditioning of large sparse finite element models.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690040204
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    Six combinations of the Ritz-Galerkin and finite element methods for elliptic boundary value problems (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 197-218 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Overall comparisons are made for six efficient combinations of the Ritz-Galerkin and finite element methods for solving elliptic boundary value problems with singularities or interfaces. The comparisons are done by using theoretical analysis and numerical experiments. Significant relations among the six combinations are also found. A survey of the six combinations and their coupling strategies are given. These combinations are important not only for matching the Ritz-Galerkin method and the finite element method but also for matching other numerical methods such as the Ritz-Galerkin method and the finite difference method.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690040304
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    Numerical solution of the Fokker Planck equation using moving finite elements (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 219-232 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Numerical solution of the Fokker Planck equation for the probability density function of a stochastic process by traditional finite difference or finite element methods produces erroneous oscillations and negative values whenever the drift is large compared to the diffusion. Upwinding schemes to eliminate the oscillations introduce false numerical diffusion because it is impossible to make the one step drift large enough to match the original equation without making the one step diffusion too large. A variation of the moving finite element method is presented that overcomes these difficulties by using basis functions that satisfy the drift part of the equation by moving along the trajectories of the deterministic dynamical system associated with the stochastic process. A Galerkin type method can then be used to find the coefficients in the remaining pure diffusion equation. Solutions of two test equations are presented to illustrate the effectiveness of the method.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690040305
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    Masthead (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988) 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690040401
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    Solution of the advection-dispersion equation with free exit boundary (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 301-313 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: I investigated the exit boundary condition for the advection-dispersion equation and found that in numerical solutions of this equation, using Galekin finite elements, a free exit boundary condition requiring no a priori information is possible, provided the advective component in the numerical equations is of sufficient magnitude relative to the dispersive component. Since the relationship between these two components is controlled by the spatial discretization through the grid Peclet number, the free exit boundary condition can in fact be applied whenever there is a non-zero advective component. The numerical solution in a finite domain with free exit boundary, using a correctly proportioned spatial discrezation, behaves like an infinite-domain solution.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690040403
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    A Tensor product generalized ADI method for the method of planes (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 283-300 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider solving separable, second order, linear elliptic prtial differential equations in three independent variables. If the partial differential opertor separates into two terms, one depending on x and y, and one depending on z, then we use the method of planes to obtain a discrete problem, which we write in tensor product from as \documentclass{article}\pagestyle{empty}\begin{document}$$ \left({T_z \otimes B_{xy} + I \otimes A_{xy} } \right)C = F $$\end{document} We apply a new interative method, the tensor product generalized alternating direction implicit method, to solve the discrete problem. We study a specific implementation that uses Hermite bicubic collocation in the xy direction and symmetric finite differences in the z direction. We demostrate that this method is a fast and accurate way to solve the large linear systems arising from three-dimensional elliptic problems.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690040402
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    Numerical methods for structured population models: The Escalator Boxcar Train (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 173-195 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A numerical integration method is introduced for the class of hyperbolic partial differential equations that occur in physiologically structured population models. These equations describe the time evolution of the population density-function over the individual state-space Ω. Exploiting the biological interpretation of the equation, this density-function is represented by a set of moments over a collection of subdomains in Ω, moving along the characteristics of the partial differential equation (PDE). These moments are readily interpreted as numbers of individuals in a cohort, mean individual state in a cohort, etc. The numerical method consists of approximating the differential equations.The method appears to be very efficient for this special type of PDE. It combines such desirable properties as as lack of dispersion and dissipation and a preservation of monotonicity of the density function along the characteristics with a strong relation to the biological background of the equations for these moments to arrive at a closed system of ordinary differential equations. The method also allows one to incorporate the usual type of nonlinearities that occur in physiologically structured population models. A numerical example is presented as an illustration of the application of the method.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690040303
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    On the numerical analysis of analytical nodal methods (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 233-254 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article presents the basic numerical analysis of the analytical nodal methods, which were originally developed in the late 1970s in relation with static and dynamic nuclear reactor calculations but are actually applicable to the numerical solution of partial differential equations (PDEs) in general, over fairly regular domains. The basic idea consists in “transverse integrating” the original PDE over all the variables minus one, leading to sets of 1D equations which are then solved in an “analytical” way, using fundamentals as well as particular solutions of the corresponding 1D operators. After examining the existing analytical methods in a critical way, we propose a more satisfactory extended analytical formalism. Superconvergence results finally lead us to useful conclusions with respect to the choice of a particular scheme.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690040306
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    Two different approaches for the treatment of boundary singularities (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 255-282 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The finite element treatment of boundary singularities in elliptic problems has demanded that special techniques be developed. Many of these use some form of singular element in the neighborhood of a singular point.For a homogenous second-order problem, defined in a domain with a polygonal boundary, we studied three cases with different singularity orders. Some results about the accuracy of the solution are presented. Numerical results have been obtained using Akin singular triangular elements with three and six nodes and quadrilateral elements having four and eight nodes. The behavior of the gradient in each of these elements is also analyzed. However, these elements are not completely satisfactory, so that an alternative technique using curved isoparametric elements is given here. The results obtained with the two methods are compared. Conclusions about numerical accuracy of each method, the order of integration and the simplicity of application are made.
    Additional Material: 28 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690040307
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    Downstream implicit schemes for advection (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 315-318 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Downstream-weighted implicit difference schemes for pure advection are stable for Courant numbers λ ≥ 1. They are numerically diffusive when λ 〉 1.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690040404
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    Stability improvement of the Euler forward method for initial value problems (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 319-327 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Euler forward method is transformed into a highly stable two-step explicit algorithm by use of a relaxation paramenter α. The stability of the new explicit family can be very high and linearly proportional to the absolute value of α. An adaptive stability approach with a matrix of parameters α is used that strongly increases the effeciency of the method. The one-dimensional finite element solutions for linear and nonlinear transient heat conduction problems show the stability, accuracy, and computational efficiency characteristics of the proposed algorithms.
    Additional Material: 7 Tab.
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    URL: http://dx.doi.org/10.1002/num.1690040405
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