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

Kh. M. Gamzaev

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 50 (2017), pp. 67-78

Résumé

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.

Détail

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