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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{VYURU_2013_6_3_a11,
     author = {N. M. Yaparova},
     title = {Numerical {Simulation} for {Solving} an {Inverse} {Boundary} {Heat} {Conduction} {Problem}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {112--124},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2013_6_3_a11/}
}
TY  - JOUR
AU  - N. M. Yaparova
TI  - Numerical Simulation for Solving an Inverse Boundary Heat Conduction Problem
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2013
SP  - 112
EP  - 124
VL  - 6
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VYURU_2013_6_3_a11/
LA  - ru
ID  - VYURU_2013_6_3_a11
ER  - 
%0 Journal Article
%A N. M. Yaparova
%T Numerical Simulation for Solving an Inverse Boundary Heat Conduction Problem
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2013
%P 112-124
%V 6
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VYURU_2013_6_3_a11/
%G ru
%F VYURU_2013_6_3_a11
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/