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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2013, Volume 6, Issue 3, Pages 112–124 (Mi vyuru12)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematical Modelling

Numerical Simulation for Solving an Inverse Boundary Heat Conduction Problem

N. M. Yaparova

South Ural State University, Chelyabinsk, Russian Federation

Abstract: This paper proposes different approaches that help to find numerical solution to the boundary problem for heat equation. The Laplace and Fourier transforms are the basis for these approaches. The application of the Laplace transform allowed us to obtain an operator equation which connected the unknown function at one boundary with the initial data on the other boundary. The approach based on the Fourier transform for a time variable enables us to get a stable solution for the inverse problem of heat diagnostics. The obtained results are used for devising numerical methods. Comparative computational analysis of these approaches shows the limits of applications and effectiveness of each numerical method.

Keywords: boundary value problems for heat equation, regularization methods, the Laplace transform, Fourier transform, method of projective regularization.

Full text: PDF file (847 kB)
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UDC: 519.6+517.9
MSC: 65N21 58J35; 35R30; 80M30
Received: 15.05.2013

Citation: N. M. Yaparova, “Numerical Simulation for Solving an Inverse Boundary Heat Conduction Problem”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 6:3 (2013), 112–124

Citation in format AMSBIB
\Bibitem{Yap13}
\by N.~M.~Yaparova
\paper Numerical Simulation for Solving an Inverse Boundary Heat Conduction Problem
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2013
\vol 6
\issue 3
\pages 112--124
\mathnet{http://mi.mathnet.ru/vyuru12}


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  • http://mi.mathnet.ru/eng/vyuru/v6/i3/p112

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. V. Solodusha, I. V. Mokry, “A numerical solution of one class of Volterra integral equations of the first kind in terms of the machine arithmetic features”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:3 (2016), 119–129  mathnet  crossref  elib
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