A KSOR solution based on the established Redlich-Kister Finite Difference for solving one dimensional diffusion problems
This paper introduces a novel approach based on the two newly established second-order Redlich-Kister Finite Difference (RKFD) discretisation scheme for solving one-dimensional (1D) diffusion problems. In the course of investigating the applicability of this methodology, the second-order RKFD discre...
| Main Authors: | , |
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| Format: | Proceedings |
| Language: | English English |
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Pusat e-pembelajaran, UMS
2023
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| Online Access: | https://eprints.ums.edu.my/id/eprint/41300/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/41300/2/FULL%20TEXT.pdf |
| _version_ | 1817926494186373120 |
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| author | Mohd Norfadli Suardi Jumat Sulaiman |
| author_facet | Mohd Norfadli Suardi Jumat Sulaiman |
| author_sort | Mohd Norfadli Suardi |
| collection | UMS |
| description | This paper introduces a novel approach based on the two newly established second-order Redlich-Kister Finite Difference (RKFD) discretisation scheme for solving one-dimensional (1D) diffusion problems. In the course of investigating the applicability of this methodology, the second-order RKFD discretisation is implemented by incorporating all derivative terms pertinent to the proposed problem, thereby rearranging it yields the second-order RKFD approximation equation. After that, the derived approximation facilitates the construction of a system of equation characterised by large-scale and sparse coefficient matrix. Considering the distinctive characteristics of this matrix, we employ two numerical methods, namely the Gauss-Seidel (GS) and Kaudd Successive Over Relaxation (KSOR) iterative methods, to iteratively solve this system of equations. To validate the applicability of the proposed method, two examples of one-dimensional diffusion are examined to confirm the efficiency of the established Redlich-Kister Finite Difference and the performance of the KSOR iterative method in comparison to the GS iterative method. The comparison between these iterative methods focuses on the number of iterations, execution time, and maximum norm. The findings of this investigation reveal that the KSOR method necessitates fewer iterations and achieves faster execution times in contrast to the GS method. |
| first_indexed | 2024-12-09T00:52:09Z |
| format | Proceedings |
| id | ums.eprints-41300 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-12-09T00:52:09Z |
| publishDate | 2023 |
| publisher | Pusat e-pembelajaran, UMS |
| record_format | dspace |
| spelling | ums.eprints-413002024-10-10T08:14:29Z https://eprints.ums.edu.my/id/eprint/41300/ A KSOR solution based on the established Redlich-Kister Finite Difference for solving one dimensional diffusion problems Mohd Norfadli Suardi Jumat Sulaiman Q1-390 Science (General) QA1-939 Mathematics This paper introduces a novel approach based on the two newly established second-order Redlich-Kister Finite Difference (RKFD) discretisation scheme for solving one-dimensional (1D) diffusion problems. In the course of investigating the applicability of this methodology, the second-order RKFD discretisation is implemented by incorporating all derivative terms pertinent to the proposed problem, thereby rearranging it yields the second-order RKFD approximation equation. After that, the derived approximation facilitates the construction of a system of equation characterised by large-scale and sparse coefficient matrix. Considering the distinctive characteristics of this matrix, we employ two numerical methods, namely the Gauss-Seidel (GS) and Kaudd Successive Over Relaxation (KSOR) iterative methods, to iteratively solve this system of equations. To validate the applicability of the proposed method, two examples of one-dimensional diffusion are examined to confirm the efficiency of the established Redlich-Kister Finite Difference and the performance of the KSOR iterative method in comparison to the GS iterative method. The comparison between these iterative methods focuses on the number of iterations, execution time, and maximum norm. The findings of this investigation reveal that the KSOR method necessitates fewer iterations and achieves faster execution times in contrast to the GS method. Pusat e-pembelajaran, UMS 2023 Proceedings PeerReviewed text en https://eprints.ums.edu.my/id/eprint/41300/1/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/41300/2/FULL%20TEXT.pdf Mohd Norfadli Suardi and Jumat Sulaiman (2023) A KSOR solution based on the established Redlich-Kister Finite Difference for solving one dimensional diffusion problems. https://oer.ums.edu.my/handle/oer_source_files/2781 |
| spellingShingle | Q1-390 Science (General) QA1-939 Mathematics Mohd Norfadli Suardi Jumat Sulaiman A KSOR solution based on the established Redlich-Kister Finite Difference for solving one dimensional diffusion problems |
| title | A KSOR solution based on the established Redlich-Kister Finite Difference for solving one dimensional diffusion problems |
| title_full | A KSOR solution based on the established Redlich-Kister Finite Difference for solving one dimensional diffusion problems |
| title_fullStr | A KSOR solution based on the established Redlich-Kister Finite Difference for solving one dimensional diffusion problems |
| title_full_unstemmed | A KSOR solution based on the established Redlich-Kister Finite Difference for solving one dimensional diffusion problems |
| title_short | A KSOR solution based on the established Redlich-Kister Finite Difference for solving one dimensional diffusion problems |
| title_sort | ksor solution based on the established redlich kister finite difference for solving one dimensional diffusion problems |
| topic | Q1-390 Science (General) QA1-939 Mathematics |
| url | https://eprints.ums.edu.my/id/eprint/41300/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/41300/2/FULL%20TEXT.pdf |
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