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heat equation; boundary value problem; integral equations; numerical solution; boundary element method
The Fourier problem on planar domains with time variable boundary is considered using integral equations. A simple numerical method for the integral equation is described and the convergence of the method is proved. It is shown how to approximate the solution of the Fourier problem and how to estimate the error. A numerical example is given.
[1] M. Dont: A note on the parabolic variation. Mathematica Bohemica (to appear). MR 1790119 | Zbl 0965.31001
[2] M. Dont: Fourier problem with bounded Baire data. Mathematica Bohemica 22 (1997), 405–441. MR 1489402 | Zbl 0898.31004
[3] M. Dont: On a heat potential. Czechoslov. Math. J. 25 (1975), 84–109. MR 0369918 | Zbl 0304.35051
[4] M. Dont: On a boundary value problem for the heat equation. Czechoslov. Math. J. 25 (1975), 110–133. MR 0369919 | Zbl 0304.35052
[5] M. Dont: A note on a heat potential and the parabolic variation. Čas. Pěst. Mat. 101 (1976), 28–44. MR 0473536 | Zbl 0325.35043
[6] M. Dont, E. Dontová: A numerical solution of the Dirichlet problem on some special doubly connected regions. Appl. Math. 43 (1998), 53–76. DOI 10.1023/A:1022296024669 | MR 1488285
[7] J. Král: Teorie potenciálu I. SPN, Praha, 1965.
[8] J. Král: Integral Operators in Potential Theory. Lecture Notes in Math. vol. 823, Springer-Verlag, 1980. MR 0590244
[9] W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling: Numerical Recipes in Pascal. Cambridge Univ. Press, 1992. MR 1034483
[10] W. L. Wendland: Boundary element methods and their asymptotic convergence. Lecture Notes of the CISM Summer-School on “Theoretical acoustic and numerical techniques”, Int. Centre Mech. Sci., Udine (Italy), P. Filippi (ed.), Springer-Verlag, Wien, New York, 1983, pp. 137–216. MR 0762829 | Zbl 0618.65109
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