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Boundary integral solutions of the heat equation


Author: E. A. McIntyre
Journal: Math. Comp. 46 (1986), 71-79, S1
MSC: Primary 65N99; Secondary 45L10, 65M99, 65R20
DOI: https://doi.org/10.1090/S0025-5718-1986-0815832-6
MathSciNet review: 815832
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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?)

  • [1] C. T. H. Baker, The Numerical Treatment of Integral Equations, Oxford Univ. Press, London, 1977. MR 0467215 (57:7079)
  • [2] J. L. Blue, "Boundary integral solutions of Laplace's equation," Bell System Tech. J., v. 57, No. 8, 1978, pp. 2797-2822. MR 508234 (80a:65240)
  • [3] 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.
  • [4] T. Cruse & F. Rizzo, eds., Boundary-Integral Equation Method: Computational Applications in Applied Mechanics, American Society of Mechanical Engineers, 1975.
  • [5] C. de Boor, A Practical Guide to Splines, Springer-Verlag, Berlin and New York, 1978. MR 507062 (80a:65027)
  • [6] 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.
  • [8] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N. J., 1964. MR 0181836 (31:6062)
  • [9] N. Ghosh, On the Convergence of the Boundary Element Method, Ph. D. Thesis, Cornell University, 1982.
  • [10] S. McKee & H. Brunner, "The repetition factor and numerical stability of Volterra integral equations," Comput. Math. Appl., v. 6, 1980, pp. 339-347. MR 604097 (82g:65064)
  • [11] J. McKenna, private discussions.
  • [12] 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)
  • [13] 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, Springer-Verlag, Berlin, 1969, pp. 23-39. MR 0273859 (42:8735)
  • [14] G. Polozhii, Equations of Mathematical Physics, Hayden, 1967.
  • [15] D. Shippy, "Application of the boundary-integral equation method to transient phenomena in solids," in [4].
  • [16] N. Schryer, A Tutorial on Galerkin's Method, using B-Splines, for Solving Differential Equations, Bell System Technical Memorandum 77-1274-1.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1986-0815832-6
Keywords: Boundary integrals, heat equation, fundamental solutions, thermal potentials, Volterra integral equations, Galerkin's method, B-splines, quadrature methods
Article copyright: © Copyright 1986 American Mathematical Society

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