A nonstationary iterated quasi-boundary value method for reconstructing the source term in a time–space fractional diffusion equation.

An inverse source problem of a time–space fractional diffusion equation is considered in this paper. Due to the ill-posedness of the inverse problem, we propose a novel nonstationary iterated quasi-boundary value regularization method for reconstructing the source function, and show that the regularization problem is well-posed. The convergence rates are established under a priori and a posterior choice rules of regularization parameters, respectively. A numerical scheme for solving the regularization problem in one-dimensional case is derived from a finite difference method. Moreover, various of numerical examples are performed to test the efficiency of our method. • A new iterated regularization method for solving ISP is proposed. • A numerical scheme for implementing the proposed method is presented. [ABSTRACT FROM AUTHOR]