Implementation of the 4EGKSOR for Solving One- Dimensional Time-Fractional Parabolic Equations with Gruenwald Implicit Difference Scheme

摘要

Solving one-dimensional time-fractional parabolic equations using numerical technique will require some iterative solver to solve the generated large and sparse linear systems. Thus, by considering the advantages of the Explicit Group iteration technique together with the Kaudd SOR (KSOR) iterative method, this paper examines the efficiency of the four-point Explicit Group Kaudd SOR (4EGKSOR) iterative method to solve the approximation equations generated from discretization of one-dimensional time-fractional parabolic equations using the finite difference scheme with the second order Grunwald Implicit difference scheme. In addition, the formulation and implementation of the proposed method to solve the problem are also presented. Numerical result and comparison with four-point Explicit Group Gauss-Seidel (4EGGS) method are given to illustrate the efficiency of the proposed method.