Determining an unknown source in a time-fractional diffusion equation based on Jacobi polynomials expansion with a modified Tiknonov regularization

Abstract

In this paper, we try to recover an unknown source in a time-fractional diffusion equation. In order to overcome the influence of boundary conditions on source conditions, we introduce the Jacobi polynomials to construct the approximation and a modified Tikhonov regularization method is proposed to deal with the illposedness. Error estimates are obtained under a discrepancy principle as the parameter choice rule. Numerical results are also presented to demonstrate the effectiveness of the proposed method.