An efficient iterative quasi-reversibility method for the inverse source problem of time-fractional diffusion equations

Abstract

This paper is devoted to recovering the source term for a time-fractional diffusion equation from additional temperature data at fixed time t = 1 . We discuss a uniqueness result of the direct problem and the ill-posedness of the inverse problem, and then apply the iterative quasi-reversibility regularization method to solve the inverse problem. Finally, some one-dimensional and two-dimensional numerical examples are given to verify the effectiveness and feasibility of the proposed method.