Chapter 16 - Computational half-sweep preconditioned Gauss–Seidel method for time-fractional diffusion equations

Abstract

In this study, we derive a finite difference approximation equation from the discretization of the one-dimensional linear time-fractional diffusion equations by using the Caputo time fractional derivative. A linear system is generated by the Caputo finite difference approximation equation. Then the resulting of the linear system is solved using the half-sweep preconditioned Gauss–Seidel (HSPGS) iterative method, and its effectiveness is compared with the existing pseconditioned Gauss–Seidel (PGS) method (known as full-sweep preconditioned Gauss–Seidel (FSPGS)) and Gauss–Seidel (GS) method. An example of the problem is presented to test the effectiveness of the proposed method. The findings of this study show that the proposed iterative method is superior compared with the FSPGS and GS methods.