Preconditioned SOR Method to Solve Time-Fractional Diffusion Equations

Abstract

This paper examines the performance of the Preconditioned SOR (PSOR) method together with an unconditionally implicit Caputo's time-fractional finite difference approximation equation for solving time-fractional partial diffusion equations (TFPDE's). To do it, the implicit Caputo's time-fractional approximation equations and preconditioned matrix are used to construct the corresponding preconditioned linear system. In addition to that, formulation and implementation the PSOR iterative method are also presented. Based on numerical results of the proposed iterative method, it can be concluded that the proposed iterative method is superior to the basic iterative methods.