The application of successive overrelaxation method for the solution of linearized half-sweep finite difference approximation to two-dimensional porous medium equation
Successive overrelaxation or S.O.R. method is a widely known parameter-based iterative method that can regulate a large and sparse system of equations so that the number of iterations required to solve the system can be reduced. Many researchers have applied the S.O.R. method to get the solution to...
| _version_ | 1825714707474939904 |
|---|---|
| author | Chew, Jackel Vui Lung Jumat Sulaiman Andang Sunarto |
| author_facet | Chew, Jackel Vui Lung Jumat Sulaiman Andang Sunarto |
| author_sort | Chew, Jackel Vui Lung |
| collection | UMS |
| description | Successive overrelaxation or S.O.R. method is a widely known parameter-based iterative method that can regulate a large and sparse system of equations so that the number of iterations required to solve the system can be reduced. Many researchers have applied the S.O.R. method to get the solution to the mathematical problem efficiently. This paper extends the application of the S.O.R. method to solve one of the nonlinear partial differential equation, which is the two-dimensional porous medium equation. The S.O.R. method is incorporated into an iterative method that is formulated based on a half-sweep finite difference approximation, and the Newton-type linearization solves the nonlinear term that presents in the equation. The numerical experiment that uses this innovative numerical method to solve several two-dimensional porous medium equation problems shows significant improvement to the percentage of reduction in the number of iterations and computation time. |
| first_indexed | 2024-03-06T03:15:49Z |
| format | Proceedings |
| id | ums.eprints-32518 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:15:49Z |
| publishDate | 2021 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | ums.eprints-325182022-05-03T13:10:02Z https://eprints.ums.edu.my/id/eprint/32518/ The application of successive overrelaxation method for the solution of linearized half-sweep finite difference approximation to two-dimensional porous medium equation Chew, Jackel Vui Lung Jumat Sulaiman Andang Sunarto QA1-43 General Successive overrelaxation or S.O.R. method is a widely known parameter-based iterative method that can regulate a large and sparse system of equations so that the number of iterations required to solve the system can be reduced. Many researchers have applied the S.O.R. method to get the solution to the mathematical problem efficiently. This paper extends the application of the S.O.R. method to solve one of the nonlinear partial differential equation, which is the two-dimensional porous medium equation. The S.O.R. method is incorporated into an iterative method that is formulated based on a half-sweep finite difference approximation, and the Newton-type linearization solves the nonlinear term that presents in the equation. The numerical experiment that uses this innovative numerical method to solve several two-dimensional porous medium equation problems shows significant improvement to the percentage of reduction in the number of iterations and computation time. IOP Publishing 2021 Proceedings PeerReviewed text en https://eprints.ums.edu.my/id/eprint/32518/2/The%20application%20of%20successive%20overrelaxation%20method%20for%20the%20solution%20of%20linearized%20half-sweep%20finite%20difference%20approximation%20to%20two-dimensional%20porous%20medium%20equation.ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/32518/1/The%20application%20of%20successive%20overrelaxation%20method%20for%20the%20solution%20of%20linearized%20half-sweep%20finite%20difference%20approximation%20to%20two-dimensional%20porous%20medium%20equation.pdf Chew, Jackel Vui Lung and Jumat Sulaiman and Andang Sunarto (2021) The application of successive overrelaxation method for the solution of linearized half-sweep finite difference approximation to two-dimensional porous medium equation. https://iopscience.iop.org/article/10.1088/1757-899X/1088/1/012002/pdf |
| spellingShingle | QA1-43 General Chew, Jackel Vui Lung Jumat Sulaiman Andang Sunarto The application of successive overrelaxation method for the solution of linearized half-sweep finite difference approximation to two-dimensional porous medium equation |
| title | The application of successive overrelaxation method for the solution of linearized half-sweep finite difference approximation to two-dimensional porous medium equation |
| title_full | The application of successive overrelaxation method for the solution of linearized half-sweep finite difference approximation to two-dimensional porous medium equation |
| title_fullStr | The application of successive overrelaxation method for the solution of linearized half-sweep finite difference approximation to two-dimensional porous medium equation |
| title_full_unstemmed | The application of successive overrelaxation method for the solution of linearized half-sweep finite difference approximation to two-dimensional porous medium equation |
| title_short | The application of successive overrelaxation method for the solution of linearized half-sweep finite difference approximation to two-dimensional porous medium equation |
| title_sort | application of successive overrelaxation method for the solution of linearized half sweep finite difference approximation to two dimensional porous medium equation |
| topic | QA1-43 General |
| url | https://eprints.ums.edu.my/id/eprint/32518/2/The%20application%20of%20successive%20overrelaxation%20method%20for%20the%20solution%20of%20linearized%20half-sweep%20finite%20difference%20approximation%20to%20two-dimensional%20porous%20medium%20equation.ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/32518/1/The%20application%20of%20successive%20overrelaxation%20method%20for%20the%20solution%20of%20linearized%20half-sweep%20finite%20difference%20approximation%20to%20two-dimensional%20porous%20medium%20equation.pdf |
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