Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Boundary integral solutions of the heat equation

Author: E. A. McIntyre
Journal: Math. Comp. 46 (1986), 71-79
MSC: Primary 65N99; Secondary 45L10, 65M99, 65R20
MathSciNet review: 815832
Full-text PDF Free Access

Abstract | References | Similar Articles | 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 (time-dependent) heat equation in two space variables.

References [Enhancements On Off] (What's this?)

  • Christopher T. H. Baker, The numerical treatment of integral equations, Clarendon Press, Oxford, 1977. Monographs on Numerical Analysis. MR 0467215
  • J. L. Blue, Boundary integral solutions of Laplace’s equation, Bell System Tech. J. 57 (1978), no. 8, 2797–2822. MR 508234, DOI
  • Y. Chang, C. Kang & D. Chen, "The use of fundamental Green’s functions for the solution of problems of heat conduction in anisotropic media," Internat. J. Heat Mass Transfer, v. 16, 1973, pp. 1905-1918. T. Cruse & F. Rizzo, eds., Boundary-Integral Equation Method: Computational Applications in Applied Mechanics, American Society of Mechanical Engineers, 1975.
  • Carl de Boor, A practical guide to splines, Applied Mathematical Sciences, vol. 27, Springer-Verlag, New York-Berlin, 1978. MR 507062
  • L. M. Delves (ed.), Numerical solution of integral equations, Clarendon Press, Oxford, 1974. A collection of papers based on the material presented at a joint Summer School in July 1973, organized by the Department of Mathematics, University of Manchester, and the Department of Computational and Statistical Science, University of Liverpool. MR 0464624
  • P. Fox, ed., The PORT Mathematical Subroutine Library, Bell Telephone Laboratories, 1976.
  • Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0181836
  • N. Ghosh, On the Convergence of the Boundary Element Method, Ph. D. Thesis, Cornell University, 1982.
  • S. McKee and H. Brunner, The repetition factor and numerical stability of Volterra integral equations, Comput. Math. Appl. 6 (1980), no. 3, 339–347. MR 604097, DOI
  • J. McKenna, private discussions.
  • S. G. Mikhlin, Integral equations and their applications to certain problems in mechanics, mathematical physics and technology, Second revised edition, The Macmillan Co., New York, 1964. Translated from the Russian by A. H. Armstrong. A Pergamon Press Book. MR 0164209
  • Ben Noble, Instability when solving Volterra integral equations of the second kind by multistep methods, Conf. on Numerical Solution of Differential Equations (Dundee, 1969) Springer, Berlin, 1969, pp. 23–39. MR 0273859
  • G. Polozhii, Equations of Mathematical Physics, Hayden, 1967. D. Shippy, "Application of the boundary-integral equation method to transient phenomena in solids," in [4]. N. Schryer, A Tutorial on Galerkin’s Method, using B-Splines, for Solving Differential Equations, Bell System Technical Memorandum 77-1274-1.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N99, 45L10, 65M99, 65R20

Retrieve articles in all journals with MSC: 65N99, 45L10, 65M99, 65R20

Additional Information

Keywords: Boundary integrals, heat equation, fundamental solutions, thermal potentials, Volterra integral equations, Galerkin’s method, <I>B</I>-splines, quadrature methods
Article copyright: © Copyright 1986 American Mathematical Society