Boundary integral solutions of the heat equation
Author:
E. A. McIntyre
Journal:
Math. Comp. 46 (1986), 7179, S1
MSC:
Primary 65N99; Secondary 45L10, 65M99, 65R20
MathSciNet review:
815832
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: The Boundary Integral Method (BIM) has recently become quite popular because of its ability to provide cheap numerical solutions to the Laplace equation. This paper describes an attempt to apply a similar approach to the (timedependent) heat equation in two space variables.
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 C. T. H. Baker, The Numerical Treatment of Integral Equations, Oxford Univ. Press, London, 1977. MR 0467215 (57:7079)
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 J. L. Blue, "Boundary integral solutions of Laplace's equation," Bell System Tech. J., v. 57, No. 8, 1978, pp. 27972822. MR 508234 (80a:65240)
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 [4]
 T. Cruse & F. Rizzo, eds., BoundaryIntegral Equation Method: Computational Applications in Applied Mechanics, American Society of Mechanical Engineers, 1975.
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 C. de Boor, A Practical Guide to Splines, SpringerVerlag, Berlin and New York, 1978. MR 507062 (80a:65027)
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 L. Delves & J. Walsh, Numerical Solution of Integral Equations, Oxford Univ. Press, London, 1974. MR 0464624 (57:4551)
 [7]
 P. Fox, ed., The PORT Mathematical Subroutine Library, Bell Telephone Laboratories, 1976.
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 A. Friedman, Partial Differential Equations of Parabolic Type, PrenticeHall, Englewood Cliffs, N. J., 1964. MR 0181836 (31:6062)
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 N. Ghosh, On the Convergence of the Boundary Element Method, Ph. D. Thesis, Cornell University, 1982.
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 S. McKee & H. Brunner, "The repetition factor and numerical stability of Volterra integral equations," Comput. Math. Appl., v. 6, 1980, pp. 339347. MR 604097 (82g:65064)
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 S. Mikhlin, Integral Equations and Their Application to Certain Problems in Mechanics, Mathematical Physics and Technology, 2nd English ed., Macmillan, New York, 1964. MR 0164209 (29:1508)
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 B. Noble, "Instability when solving Volterra integral equations of the second kind by multistep methods," in Conference on the Numerical Solutions of Differential Equations, Lecture Notes in Math., no. 109, SpringerVerlag, Berlin, 1969, pp. 2339. MR 0273859 (42:8735)
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 G. Polozhii, Equations of Mathematical Physics, Hayden, 1967.
 [15]
 D. Shippy, "Application of the boundaryintegral equation method to transient phenomena in solids," in [4].
 [16]
 N. Schryer, A Tutorial on Galerkin's Method, using BSplines, for Solving Differential Equations, Bell System Technical Memorandum 7712741.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198608158326
PII:
S 00255718(1986)08158326
Keywords:
Boundary integrals,
heat equation,
fundamental solutions,
thermal potentials,
Volterra integral equations,
Galerkin's method,
Bsplines,
quadrature methods
Article copyright:
© Copyright 1986 American Mathematical Society
