A heat approximation

Miroslav Dont

Applications of Mathematics (2000)

  • Volume: 45, Issue: 1, page 41-68
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Dont, Miroslav. "A heat approximation." Applications of Mathematics 45.1 (2000): 41-68. <http://eudml.org/doc/33048>.

@article{Dont2000,
abstract = {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.},
author = {Dont, Miroslav},
journal = {Applications of Mathematics},
keywords = {heat equation; boundary value problem; integral equations; numerical solution; boundary element method; Fourier problem; heat equation; boundary integral equation; numerical method},
language = {eng},
number = {1},
pages = {41-68},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A heat approximation},
url = {http://eudml.org/doc/33048},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Dont, Miroslav
TI - A heat approximation
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 1
SP - 41
EP - 68
AB - 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.
LA - eng
KW - heat equation; boundary value problem; integral equations; numerical solution; boundary element method; Fourier problem; heat equation; boundary integral equation; numerical method
UR - http://eudml.org/doc/33048
ER -

References

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  4. On a boundary value problem for the heat equation, Czechoslov. Math. J. 25 (1975), 110–133. (1975) Zbl0304.35052MR0369919
  5. A note on a heat potential and the parabolic variation, Čas. Pěst. Mat. 101 (1976), 28–44. (1976) Zbl0325.35043MR0473536
  6. 10.1023/A:1022296024669, Appl. Math. 43 (1998), 53–76. (1998) MR1488285DOI10.1023/A:1022296024669
  7. Teorie potenciálu I, SPN, Praha, 1965. (1965) 
  8. Integral Operators in Potential Theory, Lecture Notes in Math. vol. 823, Springer-Verlag, 1980. (1980) MR0590244
  9. Numerical Recipes in Pascal, Cambridge Univ. Press, 1992. (1992) MR1034483
  10. 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. (1983) Zbl0618.65109MR0762829

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