Four-Point EGSOR Iteration for the Grunwald Implicit Finite Difference Solution of One-Dimensional Time-Fractional Parabolic Equations

In this paper, our main concerned is on the application of the formulation of a four-point explicit group successive over-relaxation (4EGSOR) iterative method in solving one-dimensional time-fractional parabolic equations based on the second-order Grunwald implicit approximation equation. The formulation of the 4EGSOR method is constructed by using the implicit approximation equation which is derived by the Grunwald derivative operator and the implicit finite difference discretization scheme. In order to access the performance results of the 4EGSOR iterative method, another block and point iterative methods which are the four-point EGGS (4EGGS) and the Gauss-Seidel (GS) were also presented as control methods. The results of three numerical experiments show substantial improvement in terms of the number of iterations and execution time.