Numerical solution of time-dependent component with sparse structure of source term for a time fractional diffusion equation

Abstract

Abstract We consider an inverse time-dependent component of source term with sparse structure for the time fractional diffusion equation in the present paper. We prove the uniqueness of the inverse problem with nonlocal observation data by Laplace transform technique. Concerning the sparsity of the source term, we transform the inverse source problem into an elastic-net regularization optimization problem. The semi-smooth Newton method is adopted to solve the optimization problem and the superconvergence of the semi-smooth Newton algorithm is proven. Several numerical examples are tested to verify the efficiency of the algorithm.