Analysis and numerical simulation of the time fractional diffusion equation by using mimetic finite differences

This paper is devoted to the numerical treatment of time fractional diffusion equation with mixed boundary conditions. A new scheme based on the combination of the implicit finite difference method for Caputo derivative in time and the mimetic finite difference in space is considered for solving this problem. The stability analysis of the proposed scheme is given by using Von-Neumann method. The numerical results are provided to demonstrate the effectiveness of the proposed method as compared with other finite difference methods.