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Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2017, Number 50, Pages 67–78 (Mi vtgu619)  

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

MECHANICS

A numerical method for solving the coefficient inverse problem for diffusion-convection-reaction equation

Kh. M. Gamzaev

Azerbaijan State Oil and Industry University, Baku, Azerbaijan

Abstract: The two inverse problems on the restoration of coefficients for nonstationary one-dimensional diffusion–convection–reaction equation are considered. The first problem is intended to determine the convective transfer coefficient, which depends only on the time in accordance with the integral overdetermination condition. The second problem allows one to obtain the reaction rate coefficient depending on the time according to the integral overdetermination condition. To solve these problems, at first, a discretization of the time derivative is implemented and the explicit-implicit schemes are used to approximate the operators in both problems. For convective transfer operator in the first problem and reaction operator in the second problem, the explicit sheme was used. For the rest of operators in these problems, the implicit sheme was applied. As a result, both problems are reduced to the differential-difference problems with respect to the functions that depend on the spatial variable. For numerical solution of the problems obtained, a non-iterative computational algorithm is proposed. It is based on reducing of the differentialdifference problem to two direct boundary-value problems and to a linear equation with respect to unknown coefficient. The proposed method was used to carry out the numerical experiments for the model problems.

Keywords: diffusion–convection–reaction equation, coefficient inverse problem, integral overdetermination condition, differential-difference problem, explicit-implicit schemes.

DOI: https://doi.org/10.17223/19988621/50/6

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Bibliographic databases:

UDC: 532.546: 519.6
Received: 04.09.2017

Citation: Kh. M. Gamzaev, “A numerical method for solving the coefficient inverse problem for diffusion-convection-reaction equation”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2017, no. 50, 67–78

Citation in format AMSBIB
\Bibitem{Gam17}
\by Kh.~M.~Gamzaev
\paper A numerical method for solving the coefficient inverse problem for diffusion-convection-reaction equation
\jour Vestn. Tomsk. Gos. Univ. Mat. Mekh.
\yr 2017
\issue 50
\pages 67--78
\mathnet{http://mi.mathnet.ru/vtgu619}
\crossref{https://doi.org/10.17223/19988621/50/6}
\elib{https://elibrary.ru/item.asp?id=30778973}


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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. Kh. M. Gamzaev, “On one inverse problem of phase transformation in solids”, Tech. Phys., 63:8 (2018), 1087–1091  crossref  isi  scopus
  • Вестник Томского государственного университета. Математика и механика
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