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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 532.546:519.6
Kh.M. Gamzaev1, S.O. Huseynzade2, G.G. Gasimov3

A NUMERICAL METHOD TO SOLVE IDENTIFICATION PROBLEM FOR THE LOWER
COEFFICIENT AND THE SOURCE IN THE CONVECTION–REACTION EQUATION

Abstract. We consider the problem of identifying simultaneously the kinetic reaction coefficient and source function depending only on a spatial variable in one-dimensional linear convection–reaction equation. As additional conditions, a non-local integral condition for the solution of the equation and the condition of the final overdetermination are given. This problem belongs to the class of combined inverse problems. By integrating the equation using the additional integral condition, the problem is transformed to a coefficient inverse problem with local conditions. The derivative with respect to the spatial variable is discretized and a special representation is proposed for solving the resultant semi-discrete problem. As a result, for each discrete value of the spatial variable, the semidiscrete problem splits into two parts: the Cauchy problem and a linear equation with respect to the approximate value of the unknown kinetic coefficient. To determine the source function, an explicit formula is also obtained. The numerical solution of the Cauchy problem uses the implicit Euler method. Numerical experiments were carried out on the basis of the proposed method.

Keywords: convection–reaction equation, combined inverse problem, coefficient inverse problem, nonlocal integral condition, semi-discrete problem.



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1 Azerbaijan State Oil and Industry University, Baku, Azerbaijan

xan.h@rambler.ru

2 Azerbaijan State Oil and Industry University, Baku, Azerbaijan

sevilhuseynzade@gmail.com

3 Azerbaijan State Oil and Industry University, Baku, Azerbaijan

q.qasim56@gmail.com

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