Space-dependent source determination in a time-fractional diffusion equation using a local discontinuous Galerkin method

Abstract

This paper is devoted to determining a space-dependent source term in an inverse problem of the time-fractional diffusion equation. We use a method based on a finite difference scheme in time and a local discontinuous Galerkin method in space and investigate the numerical stability and convergence of the proposed method. Finally, various numerical examples are used illustrate the effectiveness and accuracy of the method.