Newton explicit decoupled group solution for two-dimensional nonlinear porous medium equation problems
This paper presents a Newton Explicit Decoupled Group method based on a half-sweep implicit finite difference scheme as an efficient solution method for two-dimensional nonlinear porous medium equation problems. The mathematical problem is subjected to the initial and Dirichlet’s boundary conditions...
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| Format: | Conference or Workshop Item |
| Language: | English English |
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Springer
2022
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| Online Access: | https://eprints.ums.edu.my/id/eprint/33408/3/Newton%20explicit%20decoupled%20group%20solution%20for%20two-dimensional%20nonlinear%20porous%20medium%20equation%20problems.pdf https://eprints.ums.edu.my/id/eprint/33408/1/Newton%20explicit%20decoupled%20group%20solution%20for%20two-dimensional%20nonlinear%20porous%20medium%20equation%20problems%20_ABSTRACT.pdf |
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| author | Chew, Jackel Vui Lung Jumat Sulaiman Andang Sunarto Fatihah Anas Muhiddin |
| author_facet | Chew, Jackel Vui Lung Jumat Sulaiman Andang Sunarto Fatihah Anas Muhiddin |
| author_sort | Chew, Jackel Vui Lung |
| collection | UMS |
| description | This paper presents a Newton Explicit Decoupled Group method based on a half-sweep implicit finite difference scheme as an efficient solution method for two-dimensional nonlinear porous medium equation problems. The mathematical problem is subjected to the initial and Dirichlet’s boundary conditions. This paper used the half-sweep technique to derive the implicit finite difference scheme to discretize the considered differential equation. The stability of the two-dimensional half-sweep finite difference approximation is analyzed. Newton method is applied to form the system of the linearized equation before the solution is approximated using the proposed Explicit Decoupled Group method. The proposed method is tested on several problems. The obtained numerical result is compared with the numerical result from the existing method from the same family of Newton-Explicit Group and the classical Newton-Gauss–Seidel method. The efficiency of the proposed method is determined based on the number of iterations and computation time. Computational complexity analysis is also reported. |
| first_indexed | 2024-03-06T03:18:13Z |
| format | Conference or Workshop Item |
| id | ums.eprints-33408 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:18:13Z |
| publishDate | 2022 |
| publisher | Springer |
| record_format | dspace |
| spelling | ums.eprints-334082022-08-03T23:16:29Z https://eprints.ums.edu.my/id/eprint/33408/ Newton explicit decoupled group solution for two-dimensional nonlinear porous medium equation problems Chew, Jackel Vui Lung Jumat Sulaiman Andang Sunarto Fatihah Anas Muhiddin QC1-999 Physics This paper presents a Newton Explicit Decoupled Group method based on a half-sweep implicit finite difference scheme as an efficient solution method for two-dimensional nonlinear porous medium equation problems. The mathematical problem is subjected to the initial and Dirichlet’s boundary conditions. This paper used the half-sweep technique to derive the implicit finite difference scheme to discretize the considered differential equation. The stability of the two-dimensional half-sweep finite difference approximation is analyzed. Newton method is applied to form the system of the linearized equation before the solution is approximated using the proposed Explicit Decoupled Group method. The proposed method is tested on several problems. The obtained numerical result is compared with the numerical result from the existing method from the same family of Newton-Explicit Group and the classical Newton-Gauss–Seidel method. The efficiency of the proposed method is determined based on the number of iterations and computation time. Computational complexity analysis is also reported. Springer 2022 Conference or Workshop Item PeerReviewed text en https://eprints.ums.edu.my/id/eprint/33408/3/Newton%20explicit%20decoupled%20group%20solution%20for%20two-dimensional%20nonlinear%20porous%20medium%20equation%20problems.pdf text en https://eprints.ums.edu.my/id/eprint/33408/1/Newton%20explicit%20decoupled%20group%20solution%20for%20two-dimensional%20nonlinear%20porous%20medium%20equation%20problems%20_ABSTRACT.pdf Chew, Jackel Vui Lung and Jumat Sulaiman and Andang Sunarto and Fatihah Anas Muhiddin (2022) Newton explicit decoupled group solution for two-dimensional nonlinear porous medium equation problems. In: Proceedings of the 8th International Conference on Computational Science and Technology: ICCST 2021, 28–29 August 2021, Labuan, Malaysia. https://link.springer.com/chapter/10.1007/978-981-16-8515-6_25 |
| spellingShingle | QC1-999 Physics Chew, Jackel Vui Lung Jumat Sulaiman Andang Sunarto Fatihah Anas Muhiddin Newton explicit decoupled group solution for two-dimensional nonlinear porous medium equation problems |
| title | Newton explicit decoupled group solution for two-dimensional nonlinear porous medium equation problems |
| title_full | Newton explicit decoupled group solution for two-dimensional nonlinear porous medium equation problems |
| title_fullStr | Newton explicit decoupled group solution for two-dimensional nonlinear porous medium equation problems |
| title_full_unstemmed | Newton explicit decoupled group solution for two-dimensional nonlinear porous medium equation problems |
| title_short | Newton explicit decoupled group solution for two-dimensional nonlinear porous medium equation problems |
| title_sort | newton explicit decoupled group solution for two dimensional nonlinear porous medium equation problems |
| topic | QC1-999 Physics |
| url | https://eprints.ums.edu.my/id/eprint/33408/3/Newton%20explicit%20decoupled%20group%20solution%20for%20two-dimensional%20nonlinear%20porous%20medium%20equation%20problems.pdf https://eprints.ums.edu.my/id/eprint/33408/1/Newton%20explicit%20decoupled%20group%20solution%20for%20two-dimensional%20nonlinear%20porous%20medium%20equation%20problems%20_ABSTRACT.pdf |
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