In this paper, we derived a finite difference approximation equation from the
discretization of the one-dimensional linear time-fractional diffusion equations with
Caputo's time-fractional derivative. A linear system is generated by implementing
Caputo's finite difference approximation equation on the specified solution domain. Then,
the linear system is solved using the proposed half-sweep preconditioned Gauss-Seidel
iterative method. The effectiveness of the method is studied, and the efficiency is
analyzed compared to the existing preconditioned Gauss-Seidel, also known as the full-sweep preconditioned Gauss-Seidel and the classic Gauss-Seidel iterative method. A few
examples of the mathematical problem are delivered to compare the performance of the
proposed and existing methods. The finding of this paper showed that the proposed
method is more efficient and effective than the full-sweep preconditioned Gauss-Seidel
and Gauss-Seidel methods.
Keywords: Caputo's fractional derivative, Implicit scheme, Half-sweep, Preconditioned, Gauss-Seidel, Iterative method
