Caputo finite difference solution for solving time-fractional diffusion equations via weighted point iteration - Mohd Usran Alibubin (e-VIBS, Faculty of Science and Natural Resources, 2024)
Time-fractional diffusion equations (TFDEs) are widely used in modeling anomalous diffusion processes, which occur in various fields such as physics, engineering, and economics. These equations offer a more accurate representation of systems where classical diffusion models fall short, particularly in capturing memory and hereditary properties of materials. In this paper, we employ the Caputo finite difference approximation equation for TFDEs by applying a discretization scheme based on the second-order implicit finite difference and Caputo fractional derivative operator. To solve these equations numerically, the one-dimensional TFDEs are discretized using Caputo’s implicit finite difference approximation. The corresponding system of linear approximation equations is then solved using weighted point iteration methods, specifically Successive Overrelaxation (SOR) and Gauss-Seidel (GS). Three examples are provided to evaluate the performance of these iterative methods. The numerical results demonstrate that the SOR method requires fewer iterations and reduces computational time, proving to be more efficient compared to the Gauss-Seidel method.