A coupled method for inverse source problem of spatial fractional anomalous diffusion equations

Based on the best perturbation method, a coupled method is developed to solve the inverse source problem of spatial fractional anomalous diffusion equation. The ill-posed inverse problem is first transformed into a well-posed problem by a Tikhonov regularization algorithm. Then the corresponding direct problem is solved by the implicit difference method, in which the source term is estimated by the best perturbation method. The efficiency and the accuracy of the proposed method are demonstrated by two numerical examples.