On quarter-sweep finite difference scheme for one-dimensional porous medium equations

• Main Authors: Jackel Chew Vui Lung, Jumat Sulaiman
• Format: Article
• Language: English
• Published: 2020
• Subjects: Q Science (General); QA Mathematics
• Online Access: https://eprints.ums.edu.my/id/eprint/25864/1/On%20quarter-sweep%20finite%20difference%20scheme%20for%20one-dimensional%20porous%20medium%20equations.pdf; https://eprints.ums.edu.my/id/eprint/25864/; https://10.12732/ijam.v33i3.6

In this article, we introduce an implicit finite difference approx-imation for one-dimensional porous medium equations using Quarter-Sweep approach. We approximate the solutions of the nonlinear porous medium equa-tions by the application of the Newton method and use the Gauss-Seidel itera-tion. This yields a numerical method that reduces the computational complex-ity when the spatial grid spaces are reduced. The numerical result shows that the proposed method has a smaller number of iterations, a shorter computation time and a good accuracy compared to Newton-Gauss-Seidel and Half-Sweep Newton-Gauss-Seidel methods.