Similarity solution of two-dimensional diffusion equations by using gauss-seidel iteration with wave variables transformation
This study aims to show the performance of Gauss-Seidel (GS) method by using similarity finite difference approximation equation to solve two-dimensional (2D) parabolic partial differential equations (PDEs) compared to Jacobi method. Similarity solution method is applied to reduce parabolic PDEs int...
| _version_ | 1825713798763249664 |
|---|---|
| author | Assis Kamu H.C. Mun Chong, Khim Phin Darmesah Gabda I.A. Seman A. Hassan N.A.J Wilaksono |
| author_facet | Assis Kamu H.C. Mun Chong, Khim Phin Darmesah Gabda I.A. Seman A. Hassan N.A.J Wilaksono |
| author_sort | Assis Kamu |
| collection | UMS |
| description | This study aims to show the performance of Gauss-Seidel (GS) method by using similarity finite difference approximation equation to solve two-dimensional (2D) parabolic partial differential equations (PDEs) compared to Jacobi method. Similarity solution method is applied to reduce parabolic PDEs into 2D explicit PDEs. A system of linear equations is generated from the discretization of 2D parabolic PDEs by using similarity finite difference scheme. Then, we present GS method for solving the system of linear equations. Besides that, the formulation and implementation of the GS method in order to solve the problem as described before are also presented. Three numerical examples are given to show the performance of GS method compared to Jacobi method. |
| first_indexed | 2024-03-06T03:02:07Z |
| format | Proceedings |
| id | ums.eprints-24560 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:02:07Z |
| publishDate | 2020 |
| publisher | Faculty of Science and Natural Resources |
| record_format | dspace |
| spelling | ums.eprints-245602021-06-09T02:12:50Z https://eprints.ums.edu.my/id/eprint/24560/ Similarity solution of two-dimensional diffusion equations by using gauss-seidel iteration with wave variables transformation Assis Kamu H.C. Mun Chong, Khim Phin Darmesah Gabda I.A. Seman A. Hassan N.A.J Wilaksono Q Science (General) QK Botany This study aims to show the performance of Gauss-Seidel (GS) method by using similarity finite difference approximation equation to solve two-dimensional (2D) parabolic partial differential equations (PDEs) compared to Jacobi method. Similarity solution method is applied to reduce parabolic PDEs into 2D explicit PDEs. A system of linear equations is generated from the discretization of 2D parabolic PDEs by using similarity finite difference scheme. Then, we present GS method for solving the system of linear equations. Besides that, the formulation and implementation of the GS method in order to solve the problem as described before are also presented. Three numerical examples are given to show the performance of GS method compared to Jacobi method. Faculty of Science and Natural Resources 2020 Proceedings PeerReviewed text en https://eprints.ums.edu.my/id/eprint/24560/1/Similarity%20solution%20of%20two-dimensional%20diffusion%20equations%20by%20using%20gauss-seidel%20iteration%20with%20wave%20variables%20transformation.pdf text en https://eprints.ums.edu.my/id/eprint/24560/2/Similarity%20solution%20of%20two-dimensional%20diffusion%20equations%20by%20using%20gauss-seidel%20iteration%20with%20wave%20variables%20transformation1.pdf Assis Kamu and H.C. Mun and Chong, Khim Phin and Darmesah Gabda and I.A. Seman and A. Hassan and N.A.J Wilaksono (2020) Similarity solution of two-dimensional diffusion equations by using gauss-seidel iteration with wave variables transformation. https://www.ums.edu.my/fssa/wp-content/uploads/2020/12/PROCEEDINGS-BOOK-ST-2020-e-ISSN.pdf |
| spellingShingle | Q Science (General) QK Botany Assis Kamu H.C. Mun Chong, Khim Phin Darmesah Gabda I.A. Seman A. Hassan N.A.J Wilaksono Similarity solution of two-dimensional diffusion equations by using gauss-seidel iteration with wave variables transformation |
| title | Similarity solution of two-dimensional diffusion equations by using gauss-seidel iteration with wave variables transformation |
| title_full | Similarity solution of two-dimensional diffusion equations by using gauss-seidel iteration with wave variables transformation |
| title_fullStr | Similarity solution of two-dimensional diffusion equations by using gauss-seidel iteration with wave variables transformation |
| title_full_unstemmed | Similarity solution of two-dimensional diffusion equations by using gauss-seidel iteration with wave variables transformation |
| title_short | Similarity solution of two-dimensional diffusion equations by using gauss-seidel iteration with wave variables transformation |
| title_sort | similarity solution of two dimensional diffusion equations by using gauss seidel iteration with wave variables transformation |
| topic | Q Science (General) QK Botany |
| url | https://eprints.ums.edu.my/id/eprint/24560/1/Similarity%20solution%20of%20two-dimensional%20diffusion%20equations%20by%20using%20gauss-seidel%20iteration%20with%20wave%20variables%20transformation.pdf https://eprints.ums.edu.my/id/eprint/24560/2/Similarity%20solution%20of%20two-dimensional%20diffusion%20equations%20by%20using%20gauss-seidel%20iteration%20with%20wave%20variables%20transformation1.pdf |
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