Solving the time fractional diffusion equations by the Half-Sweep SOR iterative method

Abstract

This paper examines the effectiveness of the combination between Successive Over-Relaxation (SOR) iterative method with the Half-Sweep (HS) iteration namely Half-Sweep Successive Over-Relaxation (HSSOR) to solve one-dimensional time fractional diffusion equation numerically. To do this, the problem will be discretized to construct the Half-Sweep finite difference approximation equation via the Caputo's time fractional derivative and implicit finite difference discretization scheme. Then a linear system will be generated by this Half-Sweep approximation equation. Next the resulting of the linear system has been solved using HSSOR iterative method in which its effectiveness will be compared with the existing Successive Over-Relaxation method (known as Full-Sweep Gauss-Seidel (FSSOR)). One example is include to examine the effectiveness the proposed method. The findings of this study point out that the HSSOR iterative method is superior in term of number of iterations and computational time as compared with the FSSOR method.