A Class of Weighted Point Schemes for the Grünwald Implicit Finite Difference Solution of Time-Fractional Parabolic Equations Using KSOR method

Abstract

In this study, system of Grünwald implicit approximation equations has been developed through the discretization of one-dimensional linear time-fractional parabolic equations using the Grünwald fractional derivative operator and second-order implicit finite difference scheme. The aim of this paper is to examine the effectiveness of Kaudd Successive Over-Relaxation (KSOR) iterative method, which is one of the weighted point iterative schemes for solving the proposed time-fractional parabolic equations by considering the Grünwald implicit approximation equation. To investigate the effectiveness of the proposed iterative method, numerical experiments and comparison are made in terms of number of iterations, execution time, 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 KSOR iterative method requires less number of iterations and execution time as compared to the existing point iterative method.