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  • Mathematics and Statistics  (64)
  • Wiley-Blackwell  (64)
  • 1985-1989  (64)
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  • 1986  (64)
  • 1950
  • 1
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    Wall effects on the slow steady motion of a particle in a viscous incompressible fluid (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 23-40 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, asymptotic expansions with respect to small Reynolds numbers are proved for the slow steady motion of an arbitrary particle in a viscous, incompressible fluid past a single plane wall. The flow problem is modelled by a certain boundary value problem for the stationary, nonlinear Navier-Stokes equations. The coefficients of these expansions are the solutions of various, linear Stokes problems which can be constructed by single layer potentials and corresponding boundary integral equations on the boundary surface of the particle. Furthermore, some asymptotic estimates at small Reynolds numbers are presented for the slow steady motion of an arbitrary particle in a viscous, incompressible fluid between two parallel, plane walls and in an infinitely long, rectilinear cylinder of arbitrary cross section.In the case of the flow problem with a single plane wall, the paper is based on a thesis, which the author has written under the guidance of Professor Dr. Wolfgang L. Wendland.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080103
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  • 2
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    Local existence of solutions of the vlasov-maxwell equations and convergence to the vlasov-poisson equations for infinite light velocity (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 533-558 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the local existence of smooth solutions for the Vlasov-Maxwell equations in three space variables. The existence time for such solutions is independent of the light velocity c. Then we derive regularity results for both the Vlasov-Poisson and the Vlasov-Maxwell equations. The last part of the paper is devoted to a proof of weak and strong convergence of the Vlasov-Maxwell equations towards the Vlasov-Poisson equations, when the light velocity c goes to infinity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080135
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  • 3
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    Masthead (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986) 
    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.1670080101
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  • 4
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    On a free boundary value problem of physical geodesy, II (existence)This paper is part of the author's “Habilitationsschrift”, accepted by the “Fachbereich 6 der Universität - Gesamthochschule - Essen”. (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), 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 determination of the figure of the earth is considered as a local free boundary value problem of potential theory. In the C1,ε-topology local existence is proved by means of Legendre transforms. This method also provides an elementary argument for the regularity of the solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080102
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  • 5
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    An optimal design problem for submerged bodies (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 50-76 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of finding the shape of a smooth body submerged in a fluid of finite depth which minimizes added mass or damping is considered. The optimal configuration is sought in a suitably constrained class so as to be physically meaningful and for which the mathematical problem of a submerged body with linearized free surface condition is uniquely solvable. The problem is formulated as a constrained optimization problem whose cost functional (e.g. added mass) is a domain functional. Continuity of the solution of the boundary value problem with respect to variations of the boundary is established in an appropriate function space setting and this is used to establish existence of an optimal solution. A variational inequality is derived for the optimal shape and it is shown how finite dimensional approximate solutions may be found.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080105
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  • 6
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    The two-dimensional, linear, orthotropic plate: The traction problem (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 102-116 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In [13] we extended the analysis of Ciarlet and Destuynder [5] to the clamped orthotropic plate. For the present paper we shall apply these methods to the orthotropic plate under traction. In particular, we shall be considering the type of problem posed in Friedrichs and Dressler [10] for the isotropic plate and make use of the fact that the variational problem will split just as was the case for the partial differential equation formulation. With the present approach we shall be able to produce a proper convergence analysis for the formal asymptotics used in Friedrichs and Dressler.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080108
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  • 7
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    On optimal shape design of systems governed by mixed Dirichlet-Signorini boundary value problems (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 157-181 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A problem for finding optimal shape for systems governed by the mixed unilateral boundary value problem of Dirichlet-Signorini-type is considered. Conditions for the solvability of the problem are stated when a variational inequality formulation and when a penalty method is used for solving the state problem in question. The asymptotic relation of design problems based on these two formulations is presented. The optimal shape design problem is discretized by means of finite element method. The convergence results for the approximation are proved. The discretized versions are then formulated as a non-linear programming problem. Results of practical computations of the problem in question are reported.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080111
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  • 8
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    Functional spaces for norton-hoff materials (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 206-222 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Some specific functional spaces are required for the study of Norton-Hoff materials. For this purpose we establish here a Korn's inequality and miscellaneous results of duality, traces, density and orthogonality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080113
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  • 9
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    A reaction-diffusion system modelling the spread of bacterial infections (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 234-246 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate a system of reaction-diffusion equations which model the spread of a bacterial infection in a human population. A decoupling technique together with global bifurcation theory is used to study the steady-state solutions of the system. The asymptotic behaviour of solutions is discussed by using sub and subersolutions and the quasimonotonicity of the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080115
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  • 10
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    Periodic solutions of quasilinear non-autonomous systems with impulses (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 247-255 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper considers a system of differential equations with impulse perturbations at fixed moments in time of the formwhere x ∊ Rn, ε is a small parameter,Sufficient conditions have been found for existence of the periodic solution of the given system in the critical and non-critical cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080116
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  • 11
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    A note on the nonlinear stability of a spatially symmetric vlasov-possion flow (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 284-288 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give sufficient conditions for the nonlinear stability of a, possibly non-smooth, spatially homogeneous Vlasov-Poisson flow.Research partially supported by Italian CNR and Ministero della Pubblica Istruzione.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080119
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  • 12
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    Optimal controllability in viscoelasticity of rate type (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 368-386 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Recently, the control engineers interest turns upon material with structural damping, such as hysteretic effects in elastoplastic systems [27] and flexible space structures [30] and in particular with damping due to the viscoelastic nature of the material, in the sense of Kelvin, [7], [12]. The reason for this renewed interest is the possibility of constructing finite rank compensators with small spillover in the observation [1], [5], [11], [25].However, a control theory for the infinite system does not seem to exist in the literature. It is shown that the trajectories, initially in a certain subspace, can be steered to rest in any time T 〉 0 using distributed load controlsThe reesults are partially contained in [19].. Furthermore, and perhaps more interesting, the L2 (0, T, H)-norm of the control decreases as T increases. This gives rise to the problem of time-optimal-controllability and the correlation to the problem of minimum norm controllability.It is shown that the time-optimal control is characterized by a weak “bang-bang” principle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080125
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  • 13
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    An algorithm for tracing the boundary curves of mushy regions in some degenerate diffusion problems (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 458-477 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present an algorithm for approximating the solution of the degenerate diffusion problem ut = (φ(u))xx in (0,1) × R+ (with zero Dirichlet boundary conditions, and nonnegative initial datum u0), where φ(u) = min {ku1} for some ϰ 〉 0. The algorithm also provides an approximation for the interface curves which represent the boundary of the Mushy Region M = {(x, t): φ (u(x, t)) = 1}. The convergence of the algorithm is proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080130
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  • 14
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    A remark on N. Korevaar's concavity maximum principle and on the asymptotic uniqueness of solutions to the plasma problem (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 93-101 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Recently N. Korevaar developed a method of proving that solutions to elliptic and parabolic boundary value problems on convex domains ω ⊂ Rn are convex functions. He introduced a concavity functionand used the classical maximum principle to prove that C ≥ 0 on ω × ω, i.e. that u is convex. Both he and independently L. Caffarelli and J. Spruck applied this method successfully to various boundary value problems. In this note we weaken the assumptions of their theorems and obtain some interesting new applications which are not covered by their previous results [CS, Ko].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080107
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  • 15
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    Distribution of resistive body-force in curved free-surface flow (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 492-501 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The customary procedure for including resistive effects in turbulent hydraulic and stratified atmospheric flows is to integrate the empirically-known boundary shears over the entire wetted boundary of a thin fluid slab. A resistive body-force is then assumed to exist everywhere in each slab to replace the boundary shearing force. For the classical Saint-Venant model, this body-force can be shown to have a constant distribution in the vertical direction, and therefore can be evaluated for use in the momentum differential equation. In the newer Dressler theory, however, for unsteady flow over curved beds, it is proved here that a constant body-force distribution is not possible. We determine its variable distribution and its magnitude for use in the curved-flow equations. This vasriable distribution acts to produce an equal resultant in every thin layer of fluid parallel to the bed in an angular wedge over the curved channel bed. The new curved-flow equations are therefore extended to include resistive effects.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670080132
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  • 16
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    On the simulation source technique for exterior problems in acousticsThis research was carried out while the second author was visiting the University of Göttingen on a Humboldt stipendium. (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 585-597 
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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 solution of the exterior Dirichlet problem for the Helmholtz equation we propose to seek the solution in the form of an acoustic single-layer potential with a distribution extended over an internal surface. This leads to an ill-posed integral equation of the first kind which can be approximately solved by the Tikhonov regularization technique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080138
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  • 17
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    Formulation variationnelle pour le calcul de la diffraction d'une onde acoustique par une surface rigide (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 598-608 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This work is a continuation of [1]. We give a space-time variational formula to the problem of the scattered acoutic wave by a hard body, using the double layer retarded potential technique. New schemes are constructed from this variationnal formula, for which we prove the stability and errors estimates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080139
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  • 18
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    Existence and uniqueness of a rayleigh surface wave propagating along the free boundary of a transversely isotropic elastic half space (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 289-310 
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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 the existence and the uniqueness of a Rayleigh surface wave propagating along the free boundary of a transversely isotropic elastic half space are proved by a spectral method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080120
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  • 19
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    On a nonlinear volterra equation (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 345-350 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Nonnegative solutions u of the nonlinear Volterra equation u = a * g(u) (g(0) = 0) in mathematical physics are considered. Under certain assumptions the nonhomogenuous equation u = a * g(u) + ƒ is studied. Some approximations of nonnegative solutions of the homogenuous equation are considered by the nonnegative solutions of the nonhomogenuous one.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080123
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  • 20
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    Generalized herglotz domains (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 451-457 
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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(θ k, α) be the far field pattern arising from the scattering of a time harmonic plane acoustic wave of wave number k and direction a by a sound-soft cylinder of cross section D. Suppose F has the Fourier expansionwhere an = an(k, . Then if ϰ2 is a Dirichlet eigenvalue for D, sufficient conditions are given on D for the existence of a nontrivial sequence |bn| where the bn are independent of such that for all directions Domains for which this is true are called generalized Herglotz domains. The conditions for a domain to be a generalized Herglotz domain are given either in terms of the Schwarz function for the analytic boundary ϱD or in terms of the Rayleigh hypothesis in acoustic scattering theory and examples are given showing the applicability of these conditions.
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    URL: http://dx.doi.org/10.1002/mma.1670080129
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  • 21
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    A justification of the one-dimensional linear model of elastic beam (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 502-515 
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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 prove that the one-dimensional model of elastic beam is an approximation to the three-dimensional linear theory of elasticity.
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    URL: http://dx.doi.org/10.1002/mma.1670080133
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  • 22
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    Stationary, oscillatory and solitary wave type solution of singular nonlinear schrödinger equations (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 559-575 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is proven that for a certain class of singular nonlinear Schrödinger equations there exist stationary ground state and oscillatory solutions. Furthermore the existence of those solitary wave type solutions is considered which do not necessarely vanish at infinity. The results are applied to problems from plasma physics; to superfluid films, and to the Heisenberg ferromagnet spin chain.
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    URL: http://dx.doi.org/10.1002/mma.1670080136
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  • 23
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    A boundary integral equation method for three-dimensional crack problems in elasticity (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 609-623 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper presents a solution procedure for three-dimensional crack problems via first kind boundary integral equations on the crack surface. The Dirichlet (Neumann) problem is reduced to a system of integral equations for the jump of the traction (of the field) across the crack surface. The calculus of pseudodifferential operators is used to derive existence and regularity of the solutions of the integral equations. With the concept of the principal symbol and the Wiener-Hopf technique we derive the explicit behavior of the densities of the integral equations near the edge of the crack surface. Based on the detailed regularity results we show how to improve the boundary element Galerkin method for our integral equations. Quasi-optimal asymptotic estimates for the Galerkin error are given.
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    URL: http://dx.doi.org/10.1002/mma.1670080140
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    The influence of a geographical barrier on the balance of selection and migration (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 269-283 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In biology, a cline is defined as a usually gradual change in gene frequency or phenotype of a population in equilibrium, from one place to another.We define a cline as a nonconstant stable steady state solution. However, for the model studied in this paper, these two definitions coincide: a nonconstant stable steady state solution is necessarily monotone. It is proved that for small values of the penetrability of the barrier, exactly two clines exist.Since we prove that the Ω-limit set of any initial condition is a steady state solution, the information thus obtained yields a rather complete understanding of the qualitative behaviour of the solutions of the evolution problem under consideration.
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    URL: http://dx.doi.org/10.1002/mma.1670080118
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    Polarized light transfer above a reflecting surface (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 311-327 
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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 and uniqueness are established for the solution of the equation of transfer of polarized light in a homogeneous atmosphere of finite optical thickness, assuming reflection by the planetary surface. A general Lp-space formulation is adopted. The boundary value problem is first written as a vector-valued integral equation. Using monotonicity properties of the spectral radii of the integral operators involved as well as recent half-range completeness results for kinetic equations with reflective boundary conditions, the present results follow as a corollary.
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    URL: http://dx.doi.org/10.1002/mma.1670080121
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    Exterior stokes problems and decay at infinity (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 351-367 
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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 the exterior Dirichlet and Neumann problem for the 3-dimensional Stokes equations. By the use of the theory of hydrodynamical potentials, the decay at infinity can be completely characterized in the framework of weighted Sobolev spaces. The results are applied to the theory of weak solutions and to the Whitehead paradox.
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    URL: http://dx.doi.org/10.1002/mma.1670080124
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  • 27
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    Formulation variationnelle espace-temps pour le calcul par potentiel retardé de la diffraction d'une onde acoustique (I) (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 405-435 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give here a space-time variational formula to the problem of the transient acoustic scattering by a free (pressure release) surface, using the retarded potential technique. From this formula, we obtain new schemes for the calculation of the potential density. We prove stability and convergence of such schemes: these are as far as we know, the first results in that direction for such problem. The case of a hard obstacle will be treated in the second part of the paper.
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    URL: http://dx.doi.org/10.1002/mma.1670080127
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    Absorbing boundary conditions for the linearized shallow water equations (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 41-49 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A mixed problem imitating the Cauchy problem for the linearized shallow water equations is considered. This problem is also a mixed problem with perfectly absorbing conditions (cp. [1], [3]). An exact formula for the conditions has been given.
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    On an exterior boundary-value problem for the time-harmonic maxwell equations with boundary conditions for the normal components of the electric and magnetic field (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 77-92 
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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 the time-harmonic Maxwell equations with the boundary condition (ν, E) = (ν, H) = 0 in an exterior multiply connected domain. A uniqueness result by Yee for the case of a simply connected domain is extended to multiply connected domains and existence is obtained by a boundary integral equation approach.
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    On the computer implementation of a coupled boundary and finite element method for the bidimensional exterior steady stokes problem (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 117-133 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A numerical technique based on the coupling of boundary and finite element methods has been developed by the author for the steady Stokes problem in an unbounded domain. The present paper deals with the implementation of the coupled program in the two-dimensional case. Computational results are given for a particular problem which can be seen as a good test case for the accuracy of the method.
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    On the determination of the worst sampling error in a communication system for pulse-amplitude-modulated signals by solving an approximation problem (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 256-268 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A communication system for pulse-amplitude-modulated signals is considered whose impulse response is bandlimited. For a certain class of sampling errors the worst case is investigated where the sampling error of the system is such that the least mean square transmission error achieved by a suitable choice of the impulse response becomes maximal. This problem is dualized in the sense of two person game theory and thereby transferred to an equivalent approximation problem for whose solution a necessary and sufficient condition is given and applied to special cases.
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    Evolution of two concentrated vortices in a two-dimensional bounded domain (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 328-344 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: We prove that two initially concentrated vortices with opposite vorticity of an incompressible ideal fluid moving in a two-dimensional bounded domain, remain concentrated during the time. The motion of their centers converges to the solution of the point vortex model with the corresponding initial conditions.
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    On the geometric form of free boundaries satisfying a bernoulli condition. II (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 387-404 
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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 be an annular domain whose interior boundary Γ* is a known Jordan curve and whose exterior boundary Γ is a free boundary characterized by the condition that|ΔU| = 1 on Γ, where U is the capacity potential in Ω. We obtain a qualitative description of Γ involving such things as its inflection points and local maxima and minima relative to specified directions. We also extend these results to obtain qualitative properties of the free boundary when it is subjected to various geometric contraints. Our results generalize those in [1].
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    The low frequency limit for time-harmonic acoustic waves (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 436-450 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The question of convergence of the solution of the exterior Dirichlet boundary value problem of the first order system of linearized acoustics as the frequency ω tends to zero is considered. The particular difficulty of having zero as an eigenvalue is handled by introducing certain scalar characteristics that  -  if prescribed  -  imply uniqueness in the limit case ω = 0. Convergence to the static solution in a weighted L2-space is shown. Eventually the convergence result obtained can be extended to a larger class of boundary value problems of Mathematical Physics due to the structure of the argument.
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    A note on the rate of convergence for certain nonlinear evolution equations (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 479-491 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: We estimate the rate of convergence to the stationary state for evolution equations which admit many H-theorems with respect to this stationary state.
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    A free boundary problem and stability for the nonlinear beam (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 516-532 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: The stability bound for the classical nonlinear Euler beam is determined in the case that its deflection is limited by an obstacle parallel to the plane of the beam. Let a clamped or simply supported beam be axially compressed by a force P 〉 P0, where P0 denotes the critical load. So far only a linear theory has been applied to analyze the stability of the solutions in contact with the obstacle and the jumping to a different state. Utilizing a free boundary problem formulation we analytically as well as numerically answer these questions for the nonlinear beam.
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    On the scattering frequencies of time-dependent potentials (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 576-584 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper discusses the scattering frequencies associated with the scalar wave equation and a time-periodic, real, potential. It is shown that the scattering frequencies form a discrete set in the complex plane and depend continuously on the potential. Existence of the scattering frequencies is proved for periodic potentials which are perturbations of a time independent, nonnegative, potential.
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    Low frequency asymptotics for the reduced wave equation in two-dimensional exterior spaces (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 134-156 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: We consider the Dirichlet problem for the reduced wave equation ΔUx + x2Ux = 0 in a two-dimensional exterior domain with boundary C, where C consists of a finite number of smooth closed curves C1,…,Cm. The question of interest is the behavior of Ux as ϰ → 0. We show that U converges to the solution of the corresponding exterior Dirichlet problem of potential theory if the boundary data converge to a limit uniformly on C. This generalizes a well-known result of R. C. MacCamy for the case m = 1.
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    Integral equations for the Fourier-transformed boundary values for the transmission problems for right-angled wedges and octants (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 182-205 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A 4×4-system of integral equations for the Fourier transformed boundary values of the normal derivatives of the wave functions defined in the four quadrants of R2-space is derived. This system results from the scalar transmission problem with continuous passage of the boundary values of the total wave-fields and of the weighted normal derivatives corresponding to the case of magnetically polarized fields. Several equivalent systems of integral equations are deduced then which show that Banach's fixed point principle may be applied at least for slightly differing media in the four quadrants. The method, which is equivalent to a compatibility condition for holomorphic functions, may be generalized to the case of the scalar transmission problem for octants in R3-space. There a 12 × 12-system of integral equations for the Fourier transformed normal derivatives on the quarter-plane faces is established.
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    On a simulation scheme for the Boltzmann equation (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 223-233 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: A scheme for the simulation of solutions of the Boltzmann equation derived by Nanbu is investigated. Rigorous results concerning questions of justification, the computation effort and the energy fluctuations are presented.
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    On least-squares approximations to compressible flow problems (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 207-228 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
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    Topics: Mathematics
    Notes: A direct finite-element method for computer solutions of compressible potential flow problems is presented. An analysis of least-squares approximation is given, including optimal order estimates for piecewise polynomial approximation spaces. The model problem considered is that of potential flow past a cylinder. Numerical results for the model problem are given for a shock-free subsonic case.
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    An explicit finite difference solution to the convection-dispersion equationPresented at the Fifth IMACS International Symposium on Computer Methods for Partial Differential Equations. (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 229-237 
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    Keywords: Mathematics and Statistics ; Numerical Methods
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    Topics: Mathematics
    Notes: An explicit finite difference equation has been development for the solution of the convection-dispersion equation. This equation has been over the entire range of 2D/vΔx between zero and one, region where no completely satisfactory method has been previously available. No oscillations or numerical dispersion were observed in any of the solutions.
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    Discontinuities across element interfaces in the global element method (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 259-272 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article we extend the global element method formalism (Delves and Hall, 1979) for two-dimensional partial differential equations to admit the possibility of solution discontinuities across element interfaces. This extension has particular relevance to problems involving sinks and sources, such as occur in oil well or groundwater management.
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    Efficient boundary element methods for three-dimensional exterior viscous flows (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 273-297 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An efficient numerical algorithm for partial differential equations in complicated three-dimensional (3-D) geometries is developed in case of exterior viscous flows. The algorithm essentially consists of a boundary element method, where the resulting algebraic system is solved with a multigrid procedure. Our investigation covers and exact mathematical foundation, a detailed analysis of the discretization error, and some numerical tests with reasonable physical examples.
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    Masthead (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986) 
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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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    Nonreflecting upwind boundaries for hyperbolic equations (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 1-12 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is commonly, but erroneously, assumed that the best way to treat upwind (closed) boundaries in numerical approximations of hyperbolic equations consists in a literal transcription, letting the numerical value be equal to the prescribed value. This results in a total reflection of spurious solutions that may arrive at the boundary from the computing domain. Those reflected solutions cannot be distinguished from consistent solutions, and they may seriously degrade the overall accuracy. We show that modifications of this treatment of the boundary may result in the absorption of spurious solutions. The effect of the absorbing properties of these boundary schemes is analyzed in Fourier space. We also analyze their numerical stability properties, and their effect on the accuracy of solutions generated in response to a time dependent boundary condition.
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    A family of numerical methods for diffusion and reaction-diffusion equations (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 31-45 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A family of methods is developed for the numerical solution of second-order parabolic partial differential equations in one space dimension. The methods are second-, third-, or fourth-order accurate in time; five of them are seen to be L0-stable in the sense of Gourlay and Morris, while the sixth is seen to be A0-stable, The methods are tested on four problems from the literature, three diffusion problems and one reaction-diffusion problem.
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    Stability of penalty finite-element methods for nonconforming problems (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 13-29 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Penalty methods have been proposed as a viable method for enforcing interelement continuity constraints on nonconforming elements. Particularly for fourth-order problems in which C1-continuity leads to elements of high degree or complex composite elements, the use of penalty methods to enforce the C1-continuity constraint appears promising. In this study we demonstrate equivalence of the finite-element penalty method to a hybrid method and provide a stability analysis which implies that the penalty method is stable only if reduced integration of a certain order is used. Numerical experiments confirm that the penalty method fails if this condition is not met.
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    The effects of symmetric/asymmetric boundary conditions on the flow of an internally heated fluid (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 47-61 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The two-dimensional flow of an internally heated fluid in a circular vessel has been investigated by using a finite-control-volume numerical model. It has been found that, when symmetry constraints are imposed along the vertical midplane of the vessel, two distinct flow patterns can he predicted for the same operating conditions, a jet-momentum-dominated pattern and buoyancy-dominated pattern. These patterns occur in an operating region where momentum and buoyancy forces are of comparable magnitude. However, when the symmetry constraints are removed and the full vessel cross section is modeled, only the buoyancy-dominated pattern is observed. Results for the two cases are described and possible reasons for the differences in behavior are discussed.
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    Masthead (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986) 
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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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    Fourth-order accurate one-step integration methods with large imaginary stability limits (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 63-70 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
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    Topics: Mathematics
    Notes: One-step integration methods of fourth-order accuracy using an odd number of function evaluations K, to solve dy/dt = A · y, are proposed. These methods have an imaginary stability limit \documentclass{article}\pagestyle{empty}\begin{document}$ S_{1\;} = \sqrt {(K - 1)^2 - 4} $\end{document}. In the case K = 5 the Kutta-Merson method results.
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    Mixed finite element methods for the approximation of time-dependent problems (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 101-111 
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    Keywords: Mathematics and Statistics ; Numerical Methods
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    Topics: Mathematics
    Notes: A given elliptic boundary problem can, in general, be approximated by several different mixed finite element methods, depending on what physical unknowns are most desired. The use of certain mixed methods for time-dependent problems has been proposed by Johnson and Thomee [5]. We analyze here some additional mixed methods for the time-dependent case which can be used to obtain direct approximations to alternate physical quantities of interest.
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    Variational grid generation (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 71-96 
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    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Recently, variational methods have been used to numerically generate grids on geometometric objects such as plane regions, volumes, and surfaces. This article presents a new method of determining variational problems that can be used to control such properties of the grid as the spacing of the points, area or volume of the cells, and the angles between the grid lines. The methods are applied to curves, surfaces, and volumes in three-dimensional space; then segments, plane curves, and plane regions appear as special cases of the general discussion. The methods used here are simpler and clearer and provide more direct control over the grid than methods that appear elsewhere. The methods are applicable to any simply connected region or any region that can be made simply connected by inserting artificial boundaries. The methods also generalize easily to solution-adaptive methods.An important ingredient in our method is the notion of a reference grid. A reference grid is defined on a region that is simpler, but analogous to, the geometric object on which a grid is desired. Variational methods are then used to transfer the reference grid to the geometric object. This gives simple and precise control of the local properties of the grid.
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    Exact solutions to difference equation models of Burgers' equation (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 123-129 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article gives exact solutions to several difference equation models of Burgers' equation. The particular cases considered correspond to the diffusion-free, nonlinear steady-state and linear steady-state situations.
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    Finite element treatment of boundary singularities by augmentation with non-exact singular functions (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 113-121 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A two-dimensional Poisson problem which contains both an interface and a reentrant corner is considered. For this problem the singular form of the solution at the reentrant corner is not known explicitly, with the result that a (nonexact) approximation to the singular form has to be calculated. The finite element method is applied to the Poisson problem, with the test and trial function spaces augmented with the nonexact singular functions. An error analysis for the nonexact augmentation is presented.
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    Masthead (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986) 
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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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    Numerical methods for the linear Boltzmann transport equation in slab geometry (1986)
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    Numerical Methods for Partial Differential Equations 2 (1986), S. 131-151 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An iterative method for computing numerical solutions of a finite-difference system corresponding to the linear Boltzmann equation in slab geometry is presented. This iterative scheme gives a straightforward marching process starting from the given boundary and initial conditions. It is shown that with a suitable initial iteration the sequence of iterations converges monotonically to a unique solution of the finite-difference system. This monotone convergence leads to improved upper and lower bounds of the solution in each iteration, and to the well-posedness of the discrete system in the sense of Hadamard. It also leads to the convergence of the discrete system to the continuous system as the mesh size of the space-velocity-time variables approaches to zero. Under a mild restriction on the time-increment the discrete system is numerically stable, independent of the mesh-size of the space and velocity. An error estimate for the computed solution due to simultaneous initial and iteration error is obtained. Also given are some numerical results for the time-dependent and the steady-state solutions.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690020205
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    Solution of governing differential equations of vibrating cylindrical shells using B-spline functions (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 173-185 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The cubic B3-spline functions and eigenfunctions are used to obtain the approximate solution for the vibration of cylindrical shells in this paper. Unified computational schemes suited for various types of boundary conditions are formulated here. In comparison with the conventional finite elements method and finite strip method, the main features of the present method are higher accuracy, fewer unknowns, ease in programming, and economy in computer solution. The numerical results are given and compared with other numerical solutions.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690020303
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    Interior and boundary difference equations for hyperbolic differential equations (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 157-172 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Interior and boundary difference equations are derived for several hyperbolic partial differential equations by means of an integral method. The method is applied to a simple transport equation, to waves in a compressible, isentropic fluid, and to surface waves in shallow water. Boundary conditions treated are (a) a perfectly reflecting boundary, (b) an open boundary with outgoing waves and a specified incoming wave, and (c) a partially reflecting boundary. For open boundaries, the major assumption for the algorithms to be valid is that outgoing waves can be defined, an assumption equivalent to the most general statement of Sommerfeld's radiation condition. The difference equations obtained are conservative, second-order accurate, two time-level, explicit, and stable (for one-dimensional, time-dependent problems) for cΔt/Δx ≤ 1 where c is the wave speed, Δt is the temporal grid size, and Δx is the spatial grid size. Numerical calculations demonstrate the excellent accuracy of the procedure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690020302
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    A multidomain spectral approximation of elliptic equationsWork performed in the research program of the Istituto di Analisi Numerica del C.N.R.-PAVIA. (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 187-205 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A spectral approximation for the Poisson equation defined on Ω = ]-1, 1[×] -1,1[ is studied. The domain Ω is decomposed into two rectangular regions and the equation is collocated at the Legendre nodes in each domain. On the common boundary of the two subdomains, suitable conditions are imposed in order to obtain a unique solution from the resulting linear system. Different values of the discretization parameters are allowed in each rectangle. We prove the stability of the scheme and give convergence estimates. The rate of convergence in a single subdomain, depends only on the regularity of the exact solution therein. An efficient preconditioning matrix is proposed.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690020304
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    Masthead (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986) 
    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.1690020401
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    Boundary element solution of the two-dimensional groundwater flow equation with stochastic free surface boundary condition (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 237-258 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An innovative approach to the approximate solution of stochastic partial differential equations in groundwater flow is presented. The method uses a formulation of the Ito's lemma in Hilbert spaces to derive partial differential equations satisfying the moments of the solution process. Since the moments equations are deterministic, they could be solved by any analytical or numerical method existing in the literature. This permits the analysis and solution of stochastic partial differential equations occurring in two-dimensional or three-dimensional domains of any geometrical shape. The method is tested for the first time in the present paper through a practical application in a sandy phreatic aquifer at the Chalk River Nuclear Laboratories, Ontario, Canada. The equation solved is the two-dimensional LaPlace equation with a dynamic, randomly perturbed, free surface boundary condition. The moments equations are derived and solved by using the boundary integral equation method. A comparison is made with a previous analytical solution obtained by applying the randomly forced one-dimensional Boussinesq equation, and some observations on modeling procedures are given.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690020402
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    A Petrov-Galerkin method and boundary approximations for hyperbolic initial boundary-value problems (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 299-316 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Petrov-Galerkin method is used to construct a semidiscrete approximation for hyperbolic systems of equations in one space dimension. Stability is analyzed for the Cauchy problem and for an initial and boundary-value problem with positive and negative characeristic speeds of unequal magnitude. Numerical experiments are conducted on a linear problem to support the stability analysis and to compare the accuracies of various boundary approximations. Experiments on a nonlinear problem check the viability of the best boundary method.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690020405
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    Finite difference solution of viscoelastic flows by preconditioned conjugate gradients (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 2 (1986), S. 317-326 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Attention is given to preconditioned conjugate gradients in the solution of systems of partial differential equations which arise in flows of viscoelastic liquids simulated by rheological implicit models. Finite differences discretization is used together with a generalization of the incomplete Cholesky conjugate-gradient method to include asymmetric nonsingular matrices, resulted from the discretization of the kinemetic fields and the pressure recovery problem in also considered in a two-dimensional planar flow.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690020406
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