NUMERICAL ALGORITHM FOR SOLVING THE INVERSE PROBLEM OF SOURCE TERM IDENTIFICATION OF THE SUBDIFFUSION DIFFERENTIAL EQUATION UNDER STURM TYPE BOUNDARY CONDITIONS

Sultanov M.A. Misilov V.E. Sadybekov M.A.
2025 Diogenes Co. Ltd.

International Journal of Applied Mathematics
2025 #38 Issue 1S 1061 - 1084 pp.

This work is devoted to the inverse problem of source term identification for the subdiffusion differential equation under Sturm-type boundary conditions. Additional information in the form of the final overdetermination condition is given. We construct a numerical algorithm for solving the inverse problem. The algorithm is based on the biconjugate gradient stabilized iterative method and the Tikhonov regularization method. To solve the forward initial boundary value subproblems at each iteration, we apply the finite difference scheme. We present the results of numerical experiments that confirm the ability of the developed algorithm to solve the inverse problem in the case of perturbations in input data.

conjugate gradient method , finite difference scheme , fractional differential equations , inverse and ill-posed problems , numerical algorithms , Sturm type boundary conditions

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Khoja Akhmet Yassawi International Kazakh-Turkish University, B. Sattarhanov Street 29, Turkestan, 160200, Kazakhstan
Krasovskii Institute of Mathematics and Mechanics, Ural Branch of RAS, S. Kovalevskaya Street 16, Ekaterinburg, 620108, Russian Federation
Ural Federal University, Mira Street 19, Ekaterinburg, 620002, Russian Federation
Institute of Mathematics and Mathematical Modeling, 125 Pushkin street, Almaty, 050010, Kazakhstan

Khoja Akhmet Yassawi International Kazakh-Turkish University
Krasovskii Institute of Mathematics and Mechanics
Ural Federal University
Institute of Mathematics and Mathematical Modeling

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