Half-sweep newton-gauss-Seidel for implicit finite difference solution of 1d nonlinear porous medium equations
This paper proposes a new numerical technique called Half-Sweep Newton-Gauss-Seidel (HSNGS) iterative method in solvingone-dimensional nonlinear porous medium equations. The general form of porous medium equation (PME) is discretized by using implicit finite difference scheme which leads to a nonlin...
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| Format: | Article |
| Language: | English English |
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Research India Publications
2016
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| Online Access: | https://eprints.ums.edu.my/id/eprint/34515/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/34515/2/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 | This paper proposes a new numerical technique called Half-Sweep Newton-Gauss-Seidel (HSNGS) iterative method in solvingone-dimensional nonlinear porous medium equations. The general form of porous medium equation (PME) is discretized by using implicit finite difference scheme which leads to a nonlinear finite difference approximation equation. The developed system of nonlinear equations is transformed by the application of Newton method into the corresponding system of linear equations. The numerical solutions are obtained by HSNGS iteration. Four illustrative examples are chosen in order to show the effectiveness of the proposed technique. The numerical results are compared with the Full-Sweep Newton-Gauss-Seidel (FSNGS) to demonstrate the applicability of the proposed iterative method. The HSNGS iterative method shows superiority in term of iteration number and computational time. |
| first_indexed | 2024-03-06T03:21:10Z |
| format | Article |
| id | ums.eprints-34515 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:21:10Z |
| publishDate | 2016 |
| publisher | Research India Publications |
| record_format | dspace |
| spelling | ums.eprints-345152022-10-20T03:20:41Z https://eprints.ums.edu.my/id/eprint/34515/ Half-sweep newton-gauss-Seidel for implicit finite difference solution of 1d nonlinear porous medium equations Chew, Jackel Vui Lung Jumat Sulaiman QA1-939 Mathematics This paper proposes a new numerical technique called Half-Sweep Newton-Gauss-Seidel (HSNGS) iterative method in solvingone-dimensional nonlinear porous medium equations. The general form of porous medium equation (PME) is discretized by using implicit finite difference scheme which leads to a nonlinear finite difference approximation equation. The developed system of nonlinear equations is transformed by the application of Newton method into the corresponding system of linear equations. The numerical solutions are obtained by HSNGS iteration. Four illustrative examples are chosen in order to show the effectiveness of the proposed technique. The numerical results are compared with the Full-Sweep Newton-Gauss-Seidel (FSNGS) to demonstrate the applicability of the proposed iterative method. The HSNGS iterative method shows superiority in term of iteration number and computational time. Research India Publications 2016 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/34515/1/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/34515/2/FULLTEXT.pdf Chew, Jackel Vui Lung and Jumat Sulaiman (2016) Half-sweep newton-gauss-Seidel for implicit finite difference solution of 1d nonlinear porous medium equations. Global Journal of Pure and Applied Mathematics, 12 (3). pp. 2745-2752. ISSN 0973-1768 https://www.researchgate.net/publication/305278668_Half-Sweep_Newton-Gauss-Seidel_for_implicit_finite_difference_solution_of_1D_nonlinear_Porous_Medium_Equations |
| spellingShingle | QA1-939 Mathematics Chew, Jackel Vui Lung Jumat Sulaiman Half-sweep newton-gauss-Seidel for implicit finite difference solution of 1d nonlinear porous medium equations |
| title | Half-sweep newton-gauss-Seidel for implicit finite difference solution of 1d nonlinear porous medium equations |
| title_full | Half-sweep newton-gauss-Seidel for implicit finite difference solution of 1d nonlinear porous medium equations |
| title_fullStr | Half-sweep newton-gauss-Seidel for implicit finite difference solution of 1d nonlinear porous medium equations |
| title_full_unstemmed | Half-sweep newton-gauss-Seidel for implicit finite difference solution of 1d nonlinear porous medium equations |
| title_short | Half-sweep newton-gauss-Seidel for implicit finite difference solution of 1d nonlinear porous medium equations |
| title_sort | half sweep newton gauss seidel for implicit finite difference solution of 1d nonlinear porous medium equations |
| topic | QA1-939 Mathematics |
| url | https://eprints.ums.edu.my/id/eprint/34515/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/34515/2/FULLTEXT.pdf |
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