Geodesic
Numerical Simulation for Solving an Inverse Boundary Heat Conduction Problem
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 3, pp. 112-124 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, method of projective regularization.
Mots-clés : Fourier transform 
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N. M. Yaparova. Numerical Simulation for Solving an Inverse Boundary Heat Conduction Problem. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 3, pp. 112-124. http://geodesic.mathdoc.fr/item/VYURU_2013_6_3_a11/

[1] P. Jonas, A. K. Louis, “Approximate Inverse for a One-Dimensional Inverse Heat Conduction Problem”, Inverse Problems, 16 (2000), 175–185 | DOI | MR | Zbl

[2] M. Prud'homme, T. H. Hguyen, “Fourier Analysis of Conjugate Gradient Method applied to Inverse Heat Conduction Problems”, International J. of Heat and Mass Transfer, 42 (1999), 4447–4460 | DOI | Zbl

[3] M. Cialkowski, K. Grysa, “Sequential and Global Method of Solving an Inverse Problem of Heat Conduction Equation”, J. of Theoretical and Applied Mechanics, 48 (2010), 111–134

[4] M. Monde, H. Arima, W. Liu, Y. Mitutake, J. A. Hammad, “An Analytical Solution for Two-Dimensional Inverse Heat Conduction Problems Using Laplace Transform”, International J. of Heat and Mass Transfer, 46 (2003), 2135–2148 | DOI | Zbl

[5] Doetsch G., Anleitung zum praktischen gebrauch der Laplace-transformation und der Z-transformation, R. Oldenbourg, 1961, 256 pp. | MR | MR | Zbl

[6] Yaparova N. M., “Different Approaches to Solve Inverse Bonduary Value Problems of Thermal Diagnostics”, Bulletin of the South Ural State University. Series \flqq Mathematics. Mechanics. Physics\frqq, 2012, no. 34, 60–67 (in Rusian) | Zbl

[7] Lavrentiev M. M., Romanov V. G., Shishatskii S. P., Ill-Posed Problems of Mathematical Physics and Analysis, Nauka, M., 1980, 287 pp. | MR

[8] Menikhes L. D., Tanana V. P., “The Finite Dimensional Approximation for the Lavrentiev Method”, Numerical Analysis and Applications, 1:1 (1998), 416–423 (in Russian) | MR

[9] Tanana V. P., Yaparova N. M., “The Optimum in Order Method of Solving Conditionally-Correct Problems”, Numerical Analysis and Applications, 9:4 (2006), 301–316 (in Russian) | Zbl

[10] Solodusha S. V., “Automatic Control Systems Modeling by Volterra Polynomials”, Modeling and Analysis of Information System, 19:1 (2012), 60–68 (in Russian)