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Title: A heat approximation (English)
Author: Dont, Miroslav
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940
Volume: 45
Issue: 1
Year: 2000
Pages: 41-68
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: heat equation
Keyword: boundary value problem
Keyword: integral equations
Keyword: numerical solution
Keyword: boundary element method
MSC: 31A25
MSC: 35K05
MSC: 45L05
MSC: 45P05
MSC: 65N99
MSC: 65R20
idZBL: Zbl 1058.31001
idMR: MR1738895
DOI: 10.1023/A:1022236700195
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Date available: 2009-09-22T18:02:35Z
Last updated: 2015-05-20
Stable URL: http://hdl.handle.net/10338.dmlcz/134428
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Reference: [1] M. Dont: A note on the parabolic variation.Mathematica Bohemica (to appear). Zbl 0965.31001, MR 1790119
Reference: [2] M. Dont: Fourier problem with bounded Baire data.Mathematica Bohemica 22 (1997), 405–441. Zbl 0898.31004, MR 1489402
Reference: [3] M. Dont: On a heat potential.Czechoslov. Math. J. 25 (1975), 84–109. Zbl 0304.35051, MR 0369918
Reference: [4] M. Dont: On a boundary value problem for the heat equation.Czechoslov. Math. J. 25 (1975), 110–133. Zbl 0304.35052, MR 0369919
Reference: [5] M. Dont: A note on a heat potential and the parabolic variation.Čas. Pěst. Mat. 101 (1976), 28–44. Zbl 0325.35043, MR 0473536
Reference: [6] M. Dont, E. Dontová: A numerical solution of the Dirichlet problem on some special doubly connected regions.Appl. Math. 43 (1998), 53–76. MR 1488285, 10.1023/A:1022296024669
Reference: [7] J. Král: Teorie potenciálu I.SPN, Praha, 1965.
Reference: [8] J. Král: Integral Operators in Potential Theory.Lecture Notes in Math. vol. 823, Springer-Verlag, 1980. MR 0590244
Reference: [9] W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling: Numerical Recipes in Pascal.Cambridge Univ. Press, 1992. MR 1034483
Reference: [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. Zbl 0618.65109, MR 0762829
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