Preconditioned Gauss-Seidel Method for the Solution of Time-fractional Diffusion Equations

Abstract

: In this paper, we deal with the application of an unconditionally implicit finite difference approximation equation of the one-dimensional linear time fractional diffusion equations via the Caputo’s time fractional derivative. Based on this implicit approximation equation, the corresponding linear system can be generated in which its coefficient matrix is large scale and sparse. To speed up the convergence rate in solving the linear system iteratively, we construct the corresponding preconditioned linear system. Then we formulate and implement the Preconditioned Gauss-Seidel (PGS) iterative method for solving the generated linear system. One example of the problem is presented to illustrate the effectiveness of PGS method. The numerical results of this study show that the proposed iterative method is superior to the basic GS iterative method.