On quarter-sweep finite difference scheme for one-dimensional porous medium equations
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. Thi...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
2020
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| Subjects: | |
| 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 |
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| Summary: | 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. |
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