The similarity finite difference solutions for two-dimensional parabolic partial differential equations via SOR iteration
This paper purposely attempts to solve two-dimensional (2D) parabolic partial differential equations (PDEs) using iterative numerical technique. Also, we determine the capability of proposed iterative technique known as Successive Over- Relaxation (SOR) iteration compared to Gauss–Seidel (GS) iterat...
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| Format: | Conference or Workshop Item |
| Language: | English English |
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2021
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| Online Access: | https://eprints.ums.edu.my/id/eprint/30200/2/The%20Similarity%20Finite%20Difference%20Solutions%20for%20Two-Dimensional%20Parabolic%20Partial%20Differential%20Equations%20via%20SOR%20Iteration.pdf https://eprints.ums.edu.my/id/eprint/30200/5/The%20similarity%20finite%20difference%20solutions%20for%20two-dimensional%20parabolic%20partial%20differential%20equations%20via%20SOR%20iteration-Abstract.pdf |
| _version_ | 1825714313695854592 |
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| author | N. A. M. Ali Jumat Sulaiman N. S. Mohamad Azali Saudi |
| author_facet | N. A. M. Ali Jumat Sulaiman N. S. Mohamad Azali Saudi |
| author_sort | N. A. M. Ali |
| collection | UMS |
| description | This paper purposely attempts to solve two-dimensional (2D) parabolic partial differential equations (PDEs) using iterative numerical technique. Also, we determine the capability of proposed iterative technique known as Successive Over- Relaxation (SOR) iteration compared to Gauss–Seidel (GS) iteration for solving the 2D parabolic PDEs problem. Firstly, we transform the 2D parabolic PDEs into 2D elliptic PDEs then discretize it using the similarity finite difference (SFD) scheme in order to construct a SFD approximation equation. Then, the SFD approximation equation yields a large-scale and sparse linear system. Next, the linear system is solved by using the proposed iterative numerical technique as described before. Furthermore, the formulation and implementation of SOR iteration are also included. In addition to that, three numerical experiments were carried out to verify the performance of the SORiteration. Finally, the findings showthat the SORiteration performs better than the GS iteration with less iteration number and computational time. |
| first_indexed | 2024-03-06T03:09:58Z |
| format | Conference or Workshop Item |
| id | ums.eprints-30200 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:09:58Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ums.eprints-302002021-08-01T03:19:06Z https://eprints.ums.edu.my/id/eprint/30200/ The similarity finite difference solutions for two-dimensional parabolic partial differential equations via SOR iteration N. A. M. Ali Jumat Sulaiman N. S. Mohamad Azali Saudi QA Mathematics TA Engineering (General). Civil engineering (General) This paper purposely attempts to solve two-dimensional (2D) parabolic partial differential equations (PDEs) using iterative numerical technique. Also, we determine the capability of proposed iterative technique known as Successive Over- Relaxation (SOR) iteration compared to Gauss–Seidel (GS) iteration for solving the 2D parabolic PDEs problem. Firstly, we transform the 2D parabolic PDEs into 2D elliptic PDEs then discretize it using the similarity finite difference (SFD) scheme in order to construct a SFD approximation equation. Then, the SFD approximation equation yields a large-scale and sparse linear system. Next, the linear system is solved by using the proposed iterative numerical technique as described before. Furthermore, the formulation and implementation of SOR iteration are also included. In addition to that, three numerical experiments were carried out to verify the performance of the SORiteration. Finally, the findings showthat the SORiteration performs better than the GS iteration with less iteration number and computational time. 2021-03-16 Conference or Workshop Item PeerReviewed text en https://eprints.ums.edu.my/id/eprint/30200/2/The%20Similarity%20Finite%20Difference%20Solutions%20for%20Two-Dimensional%20Parabolic%20Partial%20Differential%20Equations%20via%20SOR%20Iteration.pdf text en https://eprints.ums.edu.my/id/eprint/30200/5/The%20similarity%20finite%20difference%20solutions%20for%20two-dimensional%20parabolic%20partial%20differential%20equations%20via%20SOR%20iteration-Abstract.pdf N. A. M. Ali and Jumat Sulaiman and N. S. Mohamad and Azali Saudi (2021) The similarity finite difference solutions for two-dimensional parabolic partial differential equations via SOR iteration. In: International Conference on Computational Science and Technology, ICCST 2020, 29 - 30 August 2020, Pattaya, Thailand. https://link.springer.com/chapter/10.1007%2F978-981-33-4069-5_42 |
| spellingShingle | QA Mathematics TA Engineering (General). Civil engineering (General) N. A. M. Ali Jumat Sulaiman N. S. Mohamad Azali Saudi The similarity finite difference solutions for two-dimensional parabolic partial differential equations via SOR iteration |
| title | The similarity finite difference solutions for two-dimensional parabolic partial differential equations via SOR iteration |
| title_full | The similarity finite difference solutions for two-dimensional parabolic partial differential equations via SOR iteration |
| title_fullStr | The similarity finite difference solutions for two-dimensional parabolic partial differential equations via SOR iteration |
| title_full_unstemmed | The similarity finite difference solutions for two-dimensional parabolic partial differential equations via SOR iteration |
| title_short | The similarity finite difference solutions for two-dimensional parabolic partial differential equations via SOR iteration |
| title_sort | similarity finite difference solutions for two dimensional parabolic partial differential equations via sor iteration |
| topic | QA Mathematics TA Engineering (General). Civil engineering (General) |
| url | https://eprints.ums.edu.my/id/eprint/30200/2/The%20Similarity%20Finite%20Difference%20Solutions%20for%20Two-Dimensional%20Parabolic%20Partial%20Differential%20Equations%20via%20SOR%20Iteration.pdf https://eprints.ums.edu.my/id/eprint/30200/5/The%20similarity%20finite%20difference%20solutions%20for%20two-dimensional%20parabolic%20partial%20differential%20equations%20via%20SOR%20iteration-Abstract.pdf |
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