Vestnik YuUrGU. Ser. Mat. Model. Progr., 2013, Volume 6, Issue 3, Pages 112–124
This article is cited in 1 scientific paper (total in 1 paper)
Numerical Simulation for Solving an Inverse Boundary Heat Conduction Problem
N. M. Yaparova
South Ural State University, Chelyabinsk, Russian Federation
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.
boundary value problems for heat equation, regularization methods, the Laplace transform, Fourier transform, method of projective regularization.
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MSC: 65N21 58J35; 35R30; 80M30
N. M. Yaparova, “Numerical Simulation for Solving an Inverse Boundary Heat Conduction Problem”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 6:3 (2013), 112–124
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\paper Numerical Simulation for Solving an Inverse Boundary Heat Conduction Problem
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
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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
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