Implementation QSGS iteration applied to fractional diffusion equation

Abstract

In this study, we propose approximate solution of the time-fractional diffusion equation (TFDE’s) based on a quarter-sweep implicit finite difference approximation equation. To derive this approximation equation, the Caputo’s time fractional derivative has been used to discretize the proposed problems. By using the Caputo’s finite difference approximation equation, a linear system will be generated and solved iteratively. In addition to that, formulation and implementation the Quarter-Sweep Gauss-Seidel (QSGS) 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 FSGS and HSGS iterative method.