Numerical evaluation on the solution of the porous medium equation by 4-point newton-explicit group
The porous medium equation is known as one of the nonlinear partial differential equations that are used to describe many physical phenomena involving fluid flow, mass and heat transfer, and diffusion of gas particles. The solution to this equation is important to understand the phenomena better. Wi...
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| Format: | Article |
| Language: | English English |
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Lebanese University
2021
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| Online Access: | https://eprints.ums.edu.my/id/eprint/34619/3/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/34619/2/FULLTEXT.pdf |
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| author | Chew, Jackel Vui Lung Jumat Sulaiman Fatihah Anas Muhiddin |
| author_facet | Chew, Jackel Vui Lung Jumat Sulaiman Fatihah Anas Muhiddin |
| author_sort | Chew, Jackel Vui Lung |
| collection | UMS |
| description | The porous medium equation is known as one of the nonlinear partial differential equations that are used to describe many physical phenomena involving fluid flow, mass and heat transfer, and diffusion of gas particles. The solution to this equation is important to understand the phenomena better. With the numerical method and advanced computing tools nowadays, solving nonlinear partial differential equations like the porous medium equation has gained interest from several researchers. Motivated by numerous efforts in solving porous medium equations, we propose a 4-point Newton-Explicit Group method and evaluate its efficiency to solve the one-dimensional problem of the porous medium equation. The formulation of the finite difference scheme, the derivation of the 4-point Newton-Explicit Group, and the numerical evaluation of the proposed method are presented. From the numerical study, we show that the 4-point Newton-Explicit Group method has a promising improvement in terms of efficiency when compared to the Newton-Gauss-Seidel and the 2-point Newton-Explicit Group methods. |
| first_indexed | 2024-03-06T03:21:28Z |
| format | Article |
| id | ums.eprints-34619 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:21:28Z |
| publishDate | 2021 |
| publisher | Lebanese University |
| record_format | dspace |
| spelling | ums.eprints-346192022-11-03T02:23:19Z https://eprints.ums.edu.my/id/eprint/34619/ Numerical evaluation on the solution of the porous medium equation by 4-point newton-explicit group Chew, Jackel Vui Lung Jumat Sulaiman Fatihah Anas Muhiddin QA1-43 General The porous medium equation is known as one of the nonlinear partial differential equations that are used to describe many physical phenomena involving fluid flow, mass and heat transfer, and diffusion of gas particles. The solution to this equation is important to understand the phenomena better. With the numerical method and advanced computing tools nowadays, solving nonlinear partial differential equations like the porous medium equation has gained interest from several researchers. Motivated by numerous efforts in solving porous medium equations, we propose a 4-point Newton-Explicit Group method and evaluate its efficiency to solve the one-dimensional problem of the porous medium equation. The formulation of the finite difference scheme, the derivation of the 4-point Newton-Explicit Group, and the numerical evaluation of the proposed method are presented. From the numerical study, we show that the 4-point Newton-Explicit Group method has a promising improvement in terms of efficiency when compared to the Newton-Gauss-Seidel and the 2-point Newton-Explicit Group methods. Lebanese University 2021 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/34619/3/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/34619/2/FULLTEXT.pdf Chew, Jackel Vui Lung and Jumat Sulaiman and Fatihah Anas Muhiddin (2021) Numerical evaluation on the solution of the porous medium equation by 4-point newton-explicit group. International Journal of Mathematics and Computer Science, 16. pp. 1487-1496. ISSN 1814-0432 http://ijmcs.future-in-tech.net/16.4/R-Lung.pdf |
| spellingShingle | QA1-43 General Chew, Jackel Vui Lung Jumat Sulaiman Fatihah Anas Muhiddin Numerical evaluation on the solution of the porous medium equation by 4-point newton-explicit group |
| title | Numerical evaluation on the solution of the porous medium equation by 4-point newton-explicit group |
| title_full | Numerical evaluation on the solution of the porous medium equation by 4-point newton-explicit group |
| title_fullStr | Numerical evaluation on the solution of the porous medium equation by 4-point newton-explicit group |
| title_full_unstemmed | Numerical evaluation on the solution of the porous medium equation by 4-point newton-explicit group |
| title_short | Numerical evaluation on the solution of the porous medium equation by 4-point newton-explicit group |
| title_sort | numerical evaluation on the solution of the porous medium equation by 4 point newton explicit group |
| topic | QA1-43 General |
| url | https://eprints.ums.edu.my/id/eprint/34619/3/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/34619/2/FULLTEXT.pdf |
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