NUMERICAL RECONSTRUCTION OF A SPACE-DEPENDENT SOURCE TERM FOR MULTIDIMENSIONAL SPACE-TIME FRACTIONAL DIFFUSION EQUATIONS

Abstract

In this paper, we consider the problem of identifying the unknown source function in the time-space fractional diffusion equation from the final observation data. An implicit difference technique is proposed in conjunction with the matrix transfer scheme for approximating the solution of the direct problem. The challenge pertains to an inverse scenario encompassing a nonlocal ill-posed operator. The problem under investigation is formulated as a regularized optimization problem with a least-squares cost function minimization objective. An approximation for the source function is obtained using an iterative non-stationary Tikhonov regularization approach. Three numerical examples are reported to verify the efficiency of the proposed schemes. © 2023, Publishing House of the Romanian Academy. All rights reserved.