Grünwald Implicit Solution for Solving One-Dimensional Time-Fractional Parabolic Equations Using SOR Iteration

Abstract

The aim of this paper is to examine the effectiveness of Successive Over-Relaxation (SOR) iterative method for solving one-dimensional time-fractional parabolic equations. The Grünwald fractional derivative operator and implicit finite difference scheme have been used to discretize the proposed linear time-fractional equations to construct system of Grünwald implicit approximation equation. The basic formulation and application of the SOR iterative method are also presented. To investigate the effectiveness of the proposed iterative method, numerical experiments and comparison are made based on the iteration numbers, time execution, and maximum absolute error. Based on numerical results, the accuracy of Grünwald implicit solution obtained by proposed iterative method is in excellent agreement, and it can be concluded that the proposed iterative method requires less number of iterations and execution time as compared to the Gauss-Seidel (GS) iterative method.