Numerical evaluation of quarter-sweep KSOR method to solve time-fractional parabolic equations
We study the performance of the combination of quarter-sweep iteration concept with the Kaudd Successive Over-Relaxation (KSOR) iterative method in solving the discretized one-dimensional time-fractional parabolic equation. We called the mixed of these two concepts as QSKSOR. The time-fractional der...
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Global Impact Factor
2020
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| Online Access: | https://eprints.ums.edu.my/id/eprint/27167/1/Numerical%20evaluation%20of%20quarter-sweep%20KSOR%20method%20to%20solve%20time-fractional%20parabolic%20equations-Abstract.pdf https://eprints.ums.edu.my/id/eprint/27167/2/Numerical%20evaluation%20of%20quarter-sweep%20KSOR%20method%20to%20solve%20time-fractional%20parabolic%20equations.pdf |
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| author | Fatihah Anas Muhiddin Jumat Sulaiman Andang Sunarto |
| author_facet | Fatihah Anas Muhiddin Jumat Sulaiman Andang Sunarto |
| author_sort | Fatihah Anas Muhiddin |
| collection | UMS |
| description | We study the performance of the combination of quarter-sweep iteration concept with the Kaudd Successive Over-Relaxation (KSOR) iterative method in solving the discretized one-dimensional time-fractional parabolic equation. We called the mixed of these two concepts as QSKSOR. The time-fractional derivative in Grünwald sense, together with the implicit finite difference scheme was used to discretized the tested problems to form the quarter-sweep implicit finite difference approximation equations in the sense of Grünwald type. This approximation equation of half-sweep will then generate a linear system. Next, we used the proposed QSKSOR iterative method to the generated linear systems before comparing the effectiveness between the other family of KSOR method, FSKSOR and HSKSOR with respect to the full- and half-sweep cases respectively. To do so, three examples are included. The results of this study show the superiority of the QSKSOR iterative method in terms of iteration numbers and execution time in comparison to the other two methods. |
| first_indexed | 2024-03-06T03:06:58Z |
| format | Article |
| id | ums.eprints-27167 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:06:58Z |
| publishDate | 2020 |
| publisher | Global Impact Factor |
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| spelling | ums.eprints-271672021-06-09T03:45:11Z https://eprints.ums.edu.my/id/eprint/27167/ Numerical evaluation of quarter-sweep KSOR method to solve time-fractional parabolic equations Fatihah Anas Muhiddin Jumat Sulaiman Andang Sunarto QA Mathematics We study the performance of the combination of quarter-sweep iteration concept with the Kaudd Successive Over-Relaxation (KSOR) iterative method in solving the discretized one-dimensional time-fractional parabolic equation. We called the mixed of these two concepts as QSKSOR. The time-fractional derivative in Grünwald sense, together with the implicit finite difference scheme was used to discretized the tested problems to form the quarter-sweep implicit finite difference approximation equations in the sense of Grünwald type. This approximation equation of half-sweep will then generate a linear system. Next, we used the proposed QSKSOR iterative method to the generated linear systems before comparing the effectiveness between the other family of KSOR method, FSKSOR and HSKSOR with respect to the full- and half-sweep cases respectively. To do so, three examples are included. The results of this study show the superiority of the QSKSOR iterative method in terms of iteration numbers and execution time in comparison to the other two methods. Global Impact Factor 2020-08 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/27167/1/Numerical%20evaluation%20of%20quarter-sweep%20KSOR%20method%20to%20solve%20time-fractional%20parabolic%20equations-Abstract.pdf text en https://eprints.ums.edu.my/id/eprint/27167/2/Numerical%20evaluation%20of%20quarter-sweep%20KSOR%20method%20to%20solve%20time-fractional%20parabolic%20equations.pdf Fatihah Anas Muhiddin and Jumat Sulaiman and Andang Sunarto (2020) Numerical evaluation of quarter-sweep KSOR method to solve time-fractional parabolic equations. International Journal of Engineering Trends and Technology, 1. pp. 63-69. https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85099277297&origin=inward |
| spellingShingle | QA Mathematics Fatihah Anas Muhiddin Jumat Sulaiman Andang Sunarto Numerical evaluation of quarter-sweep KSOR method to solve time-fractional parabolic equations |
| title | Numerical evaluation of quarter-sweep KSOR method to solve time-fractional parabolic equations |
| title_full | Numerical evaluation of quarter-sweep KSOR method to solve time-fractional parabolic equations |
| title_fullStr | Numerical evaluation of quarter-sweep KSOR method to solve time-fractional parabolic equations |
| title_full_unstemmed | Numerical evaluation of quarter-sweep KSOR method to solve time-fractional parabolic equations |
| title_short | Numerical evaluation of quarter-sweep KSOR method to solve time-fractional parabolic equations |
| title_sort | numerical evaluation of quarter sweep ksor method to solve time fractional parabolic equations |
| topic | QA Mathematics |
| url | https://eprints.ums.edu.my/id/eprint/27167/1/Numerical%20evaluation%20of%20quarter-sweep%20KSOR%20method%20to%20solve%20time-fractional%20parabolic%20equations-Abstract.pdf https://eprints.ums.edu.my/id/eprint/27167/2/Numerical%20evaluation%20of%20quarter-sweep%20KSOR%20method%20to%20solve%20time-fractional%20parabolic%20equations.pdf |
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