Implicit solution of 1d nonlinear porous medium equation using the four-point newton-EGMSOR iterative method
The numerical method can be a good choice in solving nonlinear partial differential equations (PDEs) due to the difficulty in finding the analytical solution. Porous medium equation (PME) is one of the nonlinear PDEs which exists in many realistic problems. This paper proposes a four-point Newton-EG...
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| Format: | Article |
| Language: | English English |
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The Publishing Office of Czestochowa University of Technology
2016
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| Online Access: | https://eprints.ums.edu.my/id/eprint/34514/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/34514/2/FULLTEXT.pdf |
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| author | Chew, Jackel Vui Lung Jumat Sulaiman |
| author_facet | Chew, Jackel Vui Lung Jumat Sulaiman |
| author_sort | Chew, Jackel Vui Lung |
| collection | UMS |
| description | The numerical method can be a good choice in solving nonlinear partial differential equations (PDEs) due to the difficulty in finding the analytical solution. Porous medium equation (PME) is one of the nonlinear PDEs which exists in many realistic problems. This paper proposes a four-point Newton-EGMSOR (4-Newton-EGMSOR) iterative method in solving 1D nonlinear PMEs. The reliability of the 4-Newton-EGMSOR iterative method in computing approximate solutions for several selected PME problems is shown with comparison to 4-Newton-EGSOR, 4-Newton-EG and Newton-Gauss-Seidel methods. Numerical results showed that the proposed method is superior in terms of the number of iterations and computational time compared to the other three tested iterative methods. |
| first_indexed | 2024-03-06T03:21:10Z |
| format | Article |
| id | ums.eprints-34514 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:21:10Z |
| publishDate | 2016 |
| publisher | The Publishing Office of Czestochowa University of Technology |
| record_format | dspace |
| spelling | ums.eprints-345142022-10-20T03:19:24Z https://eprints.ums.edu.my/id/eprint/34514/ Implicit solution of 1d nonlinear porous medium equation using the four-point newton-EGMSOR iterative method Chew, Jackel Vui Lung Jumat Sulaiman QA299.6-433 Analysis The numerical method can be a good choice in solving nonlinear partial differential equations (PDEs) due to the difficulty in finding the analytical solution. Porous medium equation (PME) is one of the nonlinear PDEs which exists in many realistic problems. This paper proposes a four-point Newton-EGMSOR (4-Newton-EGMSOR) iterative method in solving 1D nonlinear PMEs. The reliability of the 4-Newton-EGMSOR iterative method in computing approximate solutions for several selected PME problems is shown with comparison to 4-Newton-EGSOR, 4-Newton-EG and Newton-Gauss-Seidel methods. Numerical results showed that the proposed method is superior in terms of the number of iterations and computational time compared to the other three tested iterative methods. The Publishing Office of Czestochowa University of Technology 2016 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/34514/1/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/34514/2/FULLTEXT.pdf Chew, Jackel Vui Lung and Jumat Sulaiman (2016) Implicit solution of 1d nonlinear porous medium equation using the four-point newton-EGMSOR iterative method. Journal of Applied Mathematics and Computational Mechanics, 15. pp. 11-21. ISSN 2299-9965 (P-ISSN) , 2353-0588 (E-ISSN) https://amcm.pcz.pl/?id=view&volume=15&issue=2&article=2 https://doi.org/10.17512/jamcm.2016.2.02 https://doi.org/10.17512/jamcm.2016.2.02 |
| spellingShingle | QA299.6-433 Analysis Chew, Jackel Vui Lung Jumat Sulaiman Implicit solution of 1d nonlinear porous medium equation using the four-point newton-EGMSOR iterative method |
| title | Implicit solution of 1d nonlinear porous medium equation using the four-point newton-EGMSOR iterative method |
| title_full | Implicit solution of 1d nonlinear porous medium equation using the four-point newton-EGMSOR iterative method |
| title_fullStr | Implicit solution of 1d nonlinear porous medium equation using the four-point newton-EGMSOR iterative method |
| title_full_unstemmed | Implicit solution of 1d nonlinear porous medium equation using the four-point newton-EGMSOR iterative method |
| title_short | Implicit solution of 1d nonlinear porous medium equation using the four-point newton-EGMSOR iterative method |
| title_sort | implicit solution of 1d nonlinear porous medium equation using the four point newton egmsor iterative method |
| topic | QA299.6-433 Analysis |
| url | https://eprints.ums.edu.my/id/eprint/34514/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/34514/2/FULLTEXT.pdf |
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