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Vestn. YuUrGU. Ser. Vych. Matem. Inform., 2016, Volume 5, Issue 2, Pages 43–58 (Mi vyurv136)  

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

Computational Mathematics

Numerical method for solving an inverse problem for nonlinear parabolic equation with unknown initial conditions

N. M. Yaparova

South Ural State University, Chelyabinsk, Russian Federation

Abstract: The paper is devoted to the inverse problem for a nonlinear parabolic equation with unknown initial conditions. A computational scheme for solving this problem is proposed. This approach allows obtain the numerical solution in internal points of domain and the unknown boundary function. The proposed scheme is based on the using of finite-difference equations and regularization technique. We investigate the stability of computational method. We obtained the dependence of stability on the discretization steps and level error of the initial data The proposed scheme proved the basis for development of numerical method and for the computational experiment. The experimental results are also presented in this paper, and confirm the effectiveness of the method.

Keywords: inverse problem, numerical method, regularization method, error estimate, computational scheme.

DOI: https://doi.org/10.14529/cmse160204

Full text: PDF file (416 kB)
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UDC: 517.96, 517.956, 519.63
Received: 30.12.2015

Citation: N. M. Yaparova, “Numerical method for solving an inverse problem for nonlinear parabolic equation with unknown initial conditions”, Vestn. YuUrGU. Ser. Vych. Matem. Inform., 5:2 (2016), 43–58

Citation in format AMSBIB
\Bibitem{Yap16}
\by N.~M.~Yaparova
\paper Numerical method for solving an inverse problem for nonlinear parabolic equation with unknown initial conditions
\jour Vestn. YuUrGU. Ser. Vych. Matem. Inform.
\yr 2016
\vol 5
\issue 2
\pages 43--58
\mathnet{http://mi.mathnet.ru/vyurv136}
\crossref{https://doi.org/10.14529/cmse160204}
\elib{http://elibrary.ru/item.asp?id=26150800}


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    This publication is cited in the following articles:
    1. L. A. Prokudina, S. U. Turlakova, “Matematicheskoe modelirovanie statsionarnogo sostoyaniya i kolebatelnykh rezhimov oregonatora”, Vestn. YuUrGU. Ser. Vych. matem. inform., 7:1 (2018), 5–15  mathnet  crossref  elib
  • Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Vychislitelnaya Matematika i Informatika"
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