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  • Mathematics and Statistics  (63)
  • Wiley-Blackwell  (63)
  • 1985-1989  (63)
  • 1980-1984
  • 1940-1944
  • 1985  (63)
  • 1943
  • 1942
Collection
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  • Wiley-Blackwell  (63)
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  • 1985-1989  (63)
  • 1980-1984
  • 1940-1944
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  • 1
    Electronic Resource
    Electronic Resource
    Optimal bounds for bilinear forms associated with linear equations (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 518-531 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The construction of upper and lower bounds to the bilinear quantity g0, f, where f is the solution of an operator equation Tf = f0, requires either an approximation for f or one for T-1. In this paper the question of “best” approximation of T-1 by an operator of the form B = βI, where β is a real constant, is investigated for linear operators that are either self-adjoint or can be related by suitable manipulations to others that are. Particular attention is paid to a special operator, previously studied by Robinson, of importance in predicting the dynamic polarisabilities of quantum-mechanical systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070137
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  • 2
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    Finite elements for the eigenvalue problem of differential operators in unbounded intervals (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 1-39 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The eigenvalue problem for one-dimensional differential operators with a possible essential spectrum is discretized with finite elements defined on a bounded interval together with a fundamental system of the differential equation outside of the interval. A non-pollution property of the discrete spectra is proved and the error in the approximation of isolated eigenvalues and corresponding eigenvectors is estimated. The convergence of some numerical algorithms for the solution of the subsequent discrete nonlinear eigenvalue problem is proved. The method is tested in some numerical examples.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070102
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  • 3
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    On spline collocation methods for boundary integral equations in the plane (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 74-89 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Nowadays boundary elemen; methods belong to the most popular numerical methods for solving elliptic boundary value problems. They consist in the reduction of the problem to equivalent integral equations (or certain generalizations) on the boundary Γ of the given domain and the approximate solution of these boundary equations. For the numerical treatment the boundary surface is decomposed into a finite number of segments and the unknown functions are approximated by corresponding finite elements and usually determined by collocation and Galerkin procedures. One finds the least difficulties in the theoretical foundation of the convergence of Galerkin methods for certain classes of equations, whereas the convergence of collocation methods, which are mostly used in numerical computations, has yet been proved only for special equations and methods.In the present paper we analyse spline collocation methods on uniform meshes with variable collocation points for one-dimensional pseudodifferential equations on a closed curve with convolutional principal parts, which encompass many classes of boundary integral equations in the plane. We give necessary and sufficient conditions for convergence and prove asymptotic error estimates. In particular we generalize some results on nodal and midpoint collocation obtained in [2], [7] and [8].The paper is organized as follows. In Section 1 we formulate the problems and the results, Section 2 deals with spline interpolation in periodic Sobolev spaces, and in Section 3 we prove the convergence theorems for the considered collocation methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070105
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  • 4
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    A method of iterative data refinement and its applications (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 108-123 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Iterative data refinement (IDR) is a general procedure for producing a sequence of estimates of the data that would be collected by a measuring device which is idealized to a certain extent, starting from the data that are collected by an actual measuring device. Following a discussion of the fundamentals of IDR, we present a number of previously published procedures which are special cases of it. We concentrate on examples from medical imaging. In particular, we discuss beam hardening correction in x-ray computerized tomography, attenuation correction in emission computerized tomography, and compensation for missing data in reconstruction from projections. We also show that a standard method of numerical mathematics (the parallel chord method) as well as a whole family of constrained iterative restoration algorithms are special cases of IDR. Thus IDR provides a common framework within which a number of originally different looking procedures are presented and discussed. We also present a result of theoretical nature concerning the initial behavior of IDR.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070108
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  • 5
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    Zur Asymptotik der wellengleichung und der wärmeleitungsgleichung in zweidimensionalen außenräumenHerrn Professor Claus Müller zum 65. Geburtstag am 20. 2. 1985 gewidmet. (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 170-201 
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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 initial and boundary value problems for the wave equation and the heat equation with a time-independent right-hand term f in two space dimensions in the exterior of a closed curve C. In the case of Neumann's boundary condition ∂u/∂n = 0 on C, the solutions increase with a logarithmic rate as t → ∞ if ∫ fdx ≠ 0. In contrast to this, the solutions of the corresponding Dirichlet problems converge to the solution of the related static problem as t → ∞. In the case of the wave equation, these results have already been obtained by L: A. Muravei under the additional assumption that the curvature of C is positive, by using high frequency estimates for the reduced wave equation Δ U + ϰ2 U = 0. The analysis presented here is based on different methods, which can be applied to arbitrary smooth curves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070111
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  • 6
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    Asymptotic analysis of differential-delay equations and nonuniqueness of periodic solutions (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 223-237 
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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 differential-delay equation x′(t) = -αf(x(t-1)), where α is a positive parameter and f is an odd function which decays like x-r at infinity. In particular, we consider the case r ≤ 2, and prove the existence of periodic solutions with special symmetries which are different from previously known periodic solutions of minimal period 4. For r = 2 we prove sharp asymptotic estimates for the minimal periods of these solutions.Our results disprove a conjecture of R. D. Nussbaum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070114
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  • 7
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    An integral equation of elasticity (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 261-268 
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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 work a certain mixed problem in R+3 for the Lamé equations in the theory of elasticity is reduced to the integral equationAn explicit formula for the solutions is given for either Ω = {x:x2 〉 0} or Ω = {x:∥x∥〈r}. The question of smoothness of the solutions is also discused. Another formulae on Ω = {x:∥x∥〈r} are found in [5], [4]. It seems that the techniques used below allows a deeper investigation of properties of the solutions to problem (*).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070117
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  • 8
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    Addendum (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 330-331 
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    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.1670070121
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  • 9
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    Relative influence of two small parameters in non uniformly elliptic homogenization problems (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), 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: We study three elliptic problems depending on two small parameters (∊ = homogenization parameter and δ = perturbation parameter which causes non uniform ellipticity). In each case, the homogenized operator corresponding to the second order operator is independent of the way (∊, δ) → (0, 0), but the convergence results and the limit solution do depend on the relative size of ∊ and δ; the relevant parameter is δ∊-2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070125
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  • 10
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    Stable methods for an inverse problem in acoustic scattering by an obstacle and an inhomogeneous medium (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 385-415 
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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 (in two-dimensional Euclidean space) the scattering of a plane, time-harmonic acoustic wave by an inhomogeneous medium Ω with compact support and a bounded obstacle D lying completely outside of the inhomogeneous medium. We show that one may determine the shape of D and the local speed of sound in Ω from a knowledge of the asymptotic behavior of the scattered wave (i.e. the far field). This is done by considering a constrained optimization problem and employing integral equation and conformal mapping techniques.By assuming a priori that the functions which determine the shape of D and the local speed of sound in Ω lie in given compact sets, we show that the problem is stable, in the sense that the solution of the inverse scattering problem depends continuously on the far field data.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070127
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  • 11
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    On the absolutely continuous spectrum of MHD plasma confined in the flat torus (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 432-442 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The spectral properties of the linearized MHD operator are investigated applying the theory of trace class perturbation. Especially, it is shown that the essential spectrum in the positive (stable) part of the spectrum contains the absolutely continuous one and the corresponding part of the spectrum is unitarily equivalent to some multiplication operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070130
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  • 12
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    The exterior dirichlet problem for the Laplace equation (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 461-469 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Using a standard application of Green's theorem, the exterior Dirichlet problem for the Laplace equation in three dimensions is reduced to a pair of integral equations. One integral equation is of the second kind and the other is of the first kind. It is known that the integral equation of the second kind is not uniquely solvable, however, it has been demonstrated that the pair of integral equations has a unique solution. The present approach is based on the observation that the known function appearing in the integral equation of the second kind lies in a certain Banach space E which is a proper subspace of the Banach space of continuous complex-valued functions equipped with the maximum norm. Furthermore, it can be shown that the related integral operator when restricted to E has spectral radius less than unity. Consequently, a particular solution to the integral equation of the second kind can be obtained by the method of successive approximations and the unique solution to the problem is then obtained by using the integral equation of the first kind. Comparisons are made between the present algorithm and other known constructive methods. Finally, an example is supplied to illustrate the method of this paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070132
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  • 13
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    A note on the solvability of Boltzmann's equation via comparison methods (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 332-339 
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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 Cauchyproblem for the space-inhomogeneous Boltzmann equation. For the so-called soft-interaction case we prove unique local solvability, analogous to a result of Palczewski [1]. However, since in our proof a comparison argument is used rather than the familiar contraction mapping principle, we are able to extend the previously known time-interval of existence. In a final section the two main difficulties in generalizing the result are discussed in some detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070122
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    On a free boundary value problem of physical geodesy, I (uniqueness)This paper is part of the author's “Habilitationsschrift”, accepted by the “Fachbereich 6 der Universität - Gesamthochschule - Essen”. (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 269-289 
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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: the shape of a slowly rotating heavy body has to be found from the boundary data of the attracting force and its potential outside of the body, provided that an approximation to the solution is already known. In this paper a uniqueness result is proved which is local with respect to the C1-topology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070118
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    Feynman-diagramme als vektorsysteme invariantentheoretisch behandelt (compton-streuung, elektron-positron-vernichtungDiese Arbeit wurde aus Mitteln der Deutschen Forschungsgemeinschaft gefördert. (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 309-330 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Employing a special contact transformation devised by S. Lie, which takes spheres into lines, we interpret the Feynman diagrams of photon electron scattering in terms of vector systems. This gives a nice kinematic model of Compton scattering. We further compute in detail the transition probabilities of the Compton scattering process by making use of the calculus of chains of complexes from classical invariant theory rather than applying the usual Dirac-matrix technique. In the final paragraph of this paper an application of our calculations to the treatment of myon decay is indicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070120
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  • 16
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    On the existence of optimum large amplitude hydrofoil propulsion II (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 346-366 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The possibility of optimum thrust-production by means of a flexible profile is discussed using a linearized theory. By applying the theory of trace theorems and Rellich's lemma, it is shown that there exists an optimum path for the profile in every class which consists of paths having uniformly bounded amplitudes and slopes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070124
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    Taylor series for the dirac function on perturbed surfaces with applications to mechanics (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 416-425 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let H0 be the Hamiltonian of an unperturbed oscillating system and let V be a small perturbation which is analytic in a neighborhood of the surface H0 = E, E 〉 0.If H0 = H + λ V is the total Hamiltonian, we prove that there is a Taylor expansion of the Dirac function δ for small |λ|When applied to test functions which are analytic near H0 = E.The connection of this result with the classical Lagrange-Bürmann theorem and some applications to the mechanics of non-linear systems are discussed.
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    URL: http://dx.doi.org/10.1002/mma.1670070128
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    A class of explicitly resolvable evolution equations (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 426-431 
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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 a class of evolution equations with “scalar nonlinearities” and the associated steady equations. An explicit representation of solutions is obtained in terms of the solution of a scalar nonlinear functional differential equation. Convergence to an equilibrium solution is discussed.
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    URL: http://dx.doi.org/10.1002/mma.1670070129
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  • 19
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    Examples involving the geometric form of level curves of harmonic functions (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 480-485 
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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, we give, for example, a Jordan curve Γ containing exactly one local maximum and one local minimum in the y-direction, such that some level curve of the capacity potential in the exterior complement of Γ has at least n local maxima and n local minima in the y-direction, n being any prescribed number.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670070134
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  • 20
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    Die lösung der maxwellschen gleichungen durch vollständige flächenfeldsysteme (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 40-54 
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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 deals with approximation theorems for the solution of Maxwell's equations governing the mathematical description of the propagation of electromagnetic waves.The well-known results ([10]) for the Helmholtz equation are generalized to Maxwell's equations: Systems of electric (resp. magnetic) dipoles are proved to span the space of all solutions of rot H + iωE = 0, rotE - iωH = 0, with n × E prescribed on the boundary. The same result holds for the “Mie-potentials”Which can be proved by a Lemma of Mie [6].Two numerical examples for the three-dimensional boundary value problems (field of a dipole, field of reflection) are presented.
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    URL: http://dx.doi.org/10.1002/mma.1670070103
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    A fast solver for riemann problems (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 101-107 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An efficient algorithm is presented for solving the Riemann problem for a polytropic gas. It enables the user to compute the solution for all physically reasonable data. The convergence of the algorithm is proved. The accuracy of the solution is limited only by the accuracy of the computer. There is an a-priori estimation of the required number of iterations. The rate of convergence turns out to be much higher than that of the usual fixed point iteration scheme.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670070107
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    Étude asymptotique des phénomènes acoustiques dans un mélange fluide-solide thermoélastique (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 154-169 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Asymptotic study of the macroscopie behaviour of a fluid-thermoelastic solid mixture. The homogenization theory is applied to the study of small perturbations in a mixture of a thermoelastic solid and a viscous compressible fluid. There appear memory phenomena in the bulk behaviour as well as a modification in the initial data regarding the original problem. The convergence of the formal asymptotic expansion to the solution of the homogenized equations is proved.
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    URL: http://dx.doi.org/10.1002/mma.1670070110
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    Unrestricted lower bounds for eigenvalues for classes of elliptic equations and systems of equations with applications to problems in elasticity (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 210-222 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Lower bounds for the eigenvalues of some elliptic equations and elliptic systems over bounded regions are obtained. The bounds are universal in that they depend only upon the volume of the region. Specific applications include the clamped plate, the buckling problem for the clamped plate and the equations of linear elasticity.Our results are consequences of extensions of the methods of Li and Yau (Comm. Mat. Phys. 88 (1983) 309-318) who obtained such results for the eigenvalues of the fixed membrane problem.
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    URL: http://dx.doi.org/10.1002/mma.1670070113
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    On the asymptotic behaviour and stability of the solution for the Broadwell model of the Boltzmann equation in three dimensions (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 340-345 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The initial value problem for the full Broadwell model, in gas kinetic theory, is investigated. By means of a fixed point theorem an upper estimate for the solution is derived, provided that the initial values satisfy suitable a priori conditions. Since this estimate is function of the time, the asymptotic behaviour of the global solution is determined.
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    URL: http://dx.doi.org/10.1002/mma.1670070123
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    A remark on the capillary contact angle (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 383-384 
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    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.1670070126
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    Exact and approximate pulsed beam solutions of Maxwell's equations (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 443-460 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An exact solution of Maxwell's equations is constructed which represents a pulse of finite energy propagating along a given axis. To simplify the computation of such a pulse, an approximate solution is constructed as a superposition of solutions of the paraxial equation. This approximation is vectorial in nature and satisfies the divergence-free condition. The difference between the exact and approximate solutions is estimated relative to the total energy transfer of the exact solution.
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    URL: http://dx.doi.org/10.1002/mma.1670070131
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    Masthead (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985) 
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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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    URL: http://dx.doi.org/10.1002/mma.1670070101
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    Qualitative properties of the boundary derivative of the capacity potential for special classes of annular domains (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 251-259 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let U(p) denote the capacity potential in an annular domain Ω (bounded by Jordan curves). We describe the qualitative behavior of ∥Δ∥ on the line segments of ∂Ω which are arbitrary, radial, or ν-directional (for some vector ν ≠ 0) in the respective cases where Ω is a convex, starlike, or ≠-convex annular domain. We apply these results to some free-boundary extremal problems in which the capacity plus weighted area functional is minimized in restricted classes of annular domains Ω.
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    Ein eindeutigkeitssatz für strahlungslösungen eines übergangsproblems zur schwingungsgleichung mit unbeschränkter trennfläche (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 290-308 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We shall derive a Rellich-type-estimate for solutions in RN of a transmission problem associated with a second order uniformly elliptic differential operator of Helmholtz-type. The transitional surface is supposed to be unbounded and a characterization of its behaviour at infinity is given. Using this estimate, we can prove a uniqueness theorem for radiation solutions of the transmission problem.
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    Erhaltungssätze und schwache lösungen in der gasdynamik (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 470-479 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The fundamental laws of Gasdynamics can be formulated very naturally as conservation laws in the form of integral relations. This formulation includes not only continuously differentiable processes but also the very important discontinuous shocks. On the other side one has the tool of weak solutions of the differential equations of Gasdynamics due to P. D. Lax and several other authors. While the conservation laws of integral type are determined by Physics in an unique way the differential equations of Gasdynamics, even if written in divergence form, are not. Hence the question arises which form of the differential equations in the weak sense is the “correct” interpretation of the physical conservation laws. This paper tries to give an answer by investigating the connections between the two formulations. At first the integral equations of Gasdynamics are written in space-time divergence form. Thus, independently from Gasdynamics, one has Haar's lemma stating that for each weak solution of a partial differential equation (in divergence form) a corresponding integral equation of conservation law type is valid for almost every family member, the family consisting of some simple domains like spheres or squares. Moreover the converse of Haar's lemma is also true. In this paper Haar's lemma is extended to a more general class of domains. This yields that both formulations of conservation laws are essentially equivalent. Additionally a divergence definition due to C. Müller is considered. As is shown by a simple example C. Müller's divergence concept leads to a more general class of solutions, not all of them being solutions of the corresponding conservation laws.
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    On the theory of nonlinear singular integral equations of Cauchy type (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 493-517 
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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 concerns the investigation of two classes of nonlinear singular integral equations with Cauchy kernel important in the applications. There are given uniqueness and existence theorems, the last by a novel application of Schauder's fixed point theorem to this type of equations.
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    URL: http://dx.doi.org/10.1002/mma.1670070136
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    On the statistical solutions of the two-dimensional, periodic Euler equation (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 55-73 
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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 the problem to define statistical solutions for the two-dimensional, periodic Euler Equation and prove a theorem of global existence and uniqueness for a regularized version. Moreover, we deduce the existence of the Euler flow in a weak form.
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    Radial sums of ridge functions: A characterization (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 90-100 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We extend and sharpen the characterization of radial sums of ridge functions of two variables given in an earlier paper. More precisely, a bound on the degree of certain polynomials is given which depends on the angles between the ridges; not only is this bound best possible but also a converse result holds. Furthermore, variants of this characterization which hold for higher dimensional analogues are also given. These results are then applied to certain parallel am models in computed tomography to obtain more precise and otherwise improved characterizations of algorithms which commute with rigid motions.
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    On the existence of optimum large amplitude hydrofoil propulsion (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 125-153 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The possibility of optimum thrust-production by means of periodic motions of a flexible wing is discussed. The disturbance velocities are assumed to be small so that a linearized theory is valid. It is proved that when adequate constraints are put upon the amplitude of the path of the wing and on the amplitude of its slopes and curvature, an optimum path exists.
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    Stabilization and regularization for solutions of an ill posed problem for the wave equation (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 202-209 
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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 the problem of finding u: [O, T] → D(A), D(A) ⊆ H, H a Hibert space such that:Is a linear positive, self-adjoint operator with a compact inverse. The problem is well known to be illposed because uniqueness and existence generally fail. We restore the stability with an a priori bound on ∥ du(0)/dt ∥ for some particular values of T.
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    On the swelling of a glassy polymer in contact with a well-stirred solvent (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 238-250 
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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 a free boundary problem arising from a model for sorption of solvent by polymers.Existence and uniqueness of the solution are proved and some results about the asymptotic behaviour are established.
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    Remarks on perfectly absorbing boundary conditions (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 486-492 
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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 is considered. This problem is also a mixed problem with perfectly absorbing boundary conditions. A theorem about the form of the problem imitating the Cauchy problem for a scalar operator was given in [3]. Some theorems concerning perfectly absorbing boundary condition can be found in [1], [2].
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    From the editors (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. i 
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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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    A numerical study of chaos in a reaction-diffusion equation (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 13-23 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A study is made using numerical experiments to see the effect of the parameters in the explicit Euler-discretized form of a one-dimensional, nonlinear, reaction-diffusion equation. Based on a series of these experiments, one of the main results obtained is that diffusion, which is usually perceived as having a stabilizing effect, is able to produce chaotic as well as divergent numerical solutions. Furthermore, the discretization parameters are also able to produce chaotic results. From the results presented herein, it is shown that varying the parameters can produce solutions that are single numbers, periodic, aperiodic (chaos), or divergent.
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    Masthead (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985) 
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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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    Principles of electricity and economics in fluid dynamics (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 145-157 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present essential connections between electrical field decomposition and network theory, economic decentralization theory, and the work of Kron on decomposition of systems for computational fluid dynamics.
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    Finite-element stream function solutions of transonic rotational internal and external flows (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 127-144 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The finite-element method is applied to the stream function formulation of transonic flows. Numerical dissipation, necessary for the calculation of mixed flows with shocks, is introduced via the artificial compressibility method. The classical problem of double-valuedness of the mass flux versus Mach number is resolved by direct integration of the vorticity equation. Solutions are obtained for isolated airfoils, the blade-to-blade cascade equation, as well as the radial equilibrium equation governing the hub-to-shroud through flow in turbomachinery.
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    Unified approach to numerical methods, part II: Finite elements, boundary methods, and their coupling (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 159-186 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This is the second in a series of three papers devoted to the presentation of a direct procedure of analysis of numerical methods for partial differential equations. The procedure consists of applying the method of weighted residuals and then interpreting the resulting equations by means of Green's formulas for discontinuous functions. Here, the general Green's formulas for operators defined in discontinuous fields developed in the first article, are applied to formulate the method of weighted residuals for arbitrary linear operators. Finite elements, boundary methods, and general procedures for coupling finite elements and boundary methods are discussed.
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    Mixed finite element methods for computing groundwater velocities (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 195-207 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Central to the understanding of problems in water quality and quantity for effective management of water resources is the development of accurate numerical models to stimulate groundwater flows and contaminant transfer. We discuss several important difficulties arising in modeling of subsurface flow and present promising numerical procedures for alleviating these problems. Furthermore, we describe mixed-finite element techniques for accurately approximating fluid velocities, and review computational results on a variety of hydrologic problems.
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    Monotonicity and finite element methods for hyperbolic initial value problems (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 187-194 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A well known theórem about super- and subfunctions for the solution of hyperbolic initial value problems constructs differentiable functions as upper and lower bounds (see Walter [1], 21 XIII). The proof can be done by transforming the differential equation problem into a set of integral equations, using the monotonicity-properties of the arising integral operators. This proof needs an integral representation for twice differentiable functions. It is shown that this proceeding can be generalized to get upper and lower bounds in terms of finite element functions. To do this, we give an integral representation for continuous, piecewise differentiable functions, including the discontinuities of their derivatives. Then the generalization of the classical proof yields interface conditions for the finite element functions. Finally, it is demonstrated how to realize numerically these conditions.
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    A compact finite element method for elastic bodies (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 209-228 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A nonconforming finite element method is described for treating linear equilibrium problems, and a convergence proof showing second order accuracy is given. The close relationship to a related compact finite difference scheme due to Phillips and Rose [1] is examined. A Condensation technique is shown to preserve the compactness property and suggests an approach to a certain type of homogenization.
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    Masthead (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985) 
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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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    A finite element collocation method for variably saturated flows in porous media (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 229-239 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: One common formulation of Richard's equation for variably saturated flows in porous media treats pressure head as the principal unknown and moisture content as a constitutive variable. Numerical approximations to this “head-based” formulation often exhibit mass-balance errors arising from inaccuracies in the temporal discretization. This article presents a finite-element collocation scheme using a mass-conserving formulation. The article also proposes a computable index of global mass balance.
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    Unified approach to numerical methods. III. Finite differences and ordinary differential equations (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 241-258 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This is the third of a sequence of articles devoted to the presentation of a direct method of analysis recently developed by one of the authors. The approach is quite general, since it is applicable to any linear operator, symmetric or nonsymmetric, regardless of its type. In particular, the theory includes steady-state and time-dependent problems. In this article the method is applied to ordinary differential equations, which constitute a very convenient illustration of its application because the analysis can be carried out in an exhaustive manner. General algorithms which yield the exact values of the solution or its derivatives are obtained in this manner.
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    Variable trial functions and the CVBEM (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 259-278 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Complex Variable Boundary Element Method; or CVBEM will be developed with respect to a variable trial function definition over each boundary element. The benefits in using this technique are that the modeling error in matching the prescribed boundary conditions (there is no error in satisfying the Laplace equation) is reduced without the addition of nodal points to the problem discretization. Consequently, the n × n matrix requirements are not increased when using this new approach.
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    A network model for two-fluid, two-phase flow (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 295-313 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A systematic derivation is given of two-fluid conservation laws on an arbitrary network. These laws are shown to conserve the mass and total energy of the mixture in the network. Numerical simulations are presented to illustrate their use.
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    Erratum (1985)
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    Numerical Methods for Partial Differential Equations 1 (1985), S. 329-329 
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    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Two-phase laminar axisymmetric jet flow: Explicit, implicit, and split-operator approximations (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 279-294 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An hybrid Eulerian-Lagrangian numerical scheme is developed for a two-phase problem and four finite-difference schemes are compared. For this purpose, the problem of hydrodynamic and thermal interactions between a fuel spray and a mixing region of two laminar, unconfined axisymmetric jets is formulated in terms of a set of parabolic differential equations for the gas phase and a set of Lagrangian ordinary differential equations for the condensed phase. Consistent, second-order accurate hybrid numerical schemes, with the exception of the explicit scheme with an accuracy between linear and quadratic, are used to solve these equations. The subset of gas-phase equations has been solved by four different numerical methods: a predictor-corrector explicit method, a sequential implicit method, a block implicit method, and a symmetric operator-splitting method. The subsystem of liquid-phase equations is solved along the droplet trajectories by a second-order Runge-Kutta scheme. The computations have been made to predict the hydro-dynamic and thermal mixing regions of the gas phase as well as the trajectories of each individual group of droplets. In addition, the size, velocity and temperature associated with each group are predicted along these trajectories. The relative merits of the above four difference-schemes are discussed by constructing effectiveness curves. At low error tolerances, the sequential implicit method gives the best results, where for large error tolerances, the explicit and operator splitting give better results. The block implicit scheme is the least effective at all accuracy requirements.
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    On operator splitting of the Euler equations consistent with Harten's second-order accurate TVD scheme (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 315-327 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Operator splitting is necessary in order to apply Harten's second-order accurate, total-variation-diminishing (TVD) method for shock capturing to higher-dimensional problems. Here two such splittings of the Euler equations are considered. By analytical means, one splitting is shown to be inconsistent; the other, scheme satisfies a fundamental necessary condition for consistency. Numerical results from a typical blast wave calculation employing this scheme are exhibited.
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    Masthead (1985)
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    Numerical Methods for Partial Differential Equations 1 (1985) 
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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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    The natural occurrence of flux splitting in a hyperbolic setting (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 1-11 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Classical derivations of the so-called Riemann invariants for hyperbolic partial differential equations have depended upon the strong-solution concept. Thus, invariance may rigorously be guaranteed only in regions of smooth flow. In general, this is as much as can be said. However, by restricting attention to linear hyperbolic systems, it further emerges that the Riemann invariant fully justifies its title. By using distribution-theoretical arguments based on the weak-solution concept. Riemann invariants of a more generalized nature are studied. For a particular weak solution u there exists, among the equivalence class [u] of weak solutions that differ from u at most on a set of measure zero, a weak solution u whose Riemann invariant corresponding to characteristic direction λ is constant on lines C: dx/dt = λ. Moreover, every piecewise-smooth weak solution has Riemann invariants that are continuous across a finite jump discontinuity. This result is used to establish for a certain Riemann problem that the one-sided time derivative at a point of discontinuity exhibits a character usually regarded in the literature as flux splitting. This result sheds light upon the validity of some upstream-biased approximation techniques for the numerical solution of hyperbolic systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690010103
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    Unified formulation of numerical methods. I. Green's formulas for operators in discontinuous fields (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 25-44 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Applying the method of weighted residuals and then interpreting the resulting equations by means of Green's formulas for discontinuous functions, a direct method of analysis is developed. The scheme includes finite differences, finite elements, and boundary methods. This is the first of a sequence of articles in which the methodology is presented. A fundamental ingredient of the procedure are general Green's formulas for operators defined in discontinuous fields. They are developed in this first article.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690010105
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    The global element method and its extension to parabolic problems (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 45-55 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article describes the derivation of the global element method, originally proposed by Delves and Hall, using the classical Euler-Lagrange theory. The method is then extended so as to be applicable to parabolic partial differential equations. The main advantages of the method, the ease of adjusting its accuracy and applying it to problems with discontinuous coefficients and point singularities, are also discussed.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690010106
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    Masthead (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985) 
    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.1690010201
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    An analysis of alternating-direction methods for parabolic equations (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 57-70 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Alternating-direction solution procedures for parabolic partial differential equations can be developed using finite-difference, finite-element, and collocation approximations in space. Each of these methods derives from a common alternating-direction formulation. Furthermore, each method leads to an O[(Δt)2] error which is in addition to the discretization error associated with standard multidimensional solutions. However, when dealing with equations having spatially varying coefficients, some alternating-direction formulations lead to yet other errors which are O(Δt). These latter errors, and thus the accuracy of the method, depend on the structure of the mass matrix associated with the approximating method.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690010107
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    High-order difference schemes for two-dimensional elliptic equations (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 71-80 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A high-order finite-difference approximation is proposed for numerical solution of linear or quasilinear elliptic differential equation. The approximation is defined on a square mesh stencil using nine node points and has a truncation error of order h4. Several test problems, including one modeling convection-dominated flows, are solved using this and existing methods. The results clearly exhibit the superiority of the new approximation, in terms of both accuracy and computational efficiency.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690010108
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    Analysis of strain representation in linear elasticity by both singular and nonsingular finite elements (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 85-104 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690010202
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    A family of methods for the wave equation in one- and two-space dimensions (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 105-125 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A family of finite-difference methods is developed for the numerical solution of the simple wave equation. Local truncation errors are calculated for each member of the family and each is analyzed for stability. The concepts of A0 stability and L0 stability, well used in the literature on other types of partial differential equation, are discussed in relation to second-order hyperbolic equations. The numerical methods arc extended to cover two-dimensional wave equations and the methods developed in this article are tested on three problems from the literature.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690010203
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