Refinement of SOR iterative method for the linear rational finite difference solution of second-order Fredholm Integro-differential equations
The primary objective of this paper is to develop the Refinement of Successive Over-Relaxation (RSOR) method based on a three-point linear rational finite difference-quadrature discretization scheme for the numerical solution of second-order linear Fredholm integro-differential equation (FIDE). Besi...
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| Format: | Article |
| Language: | English English |
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Penerbit UPM
2022
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| Online Access: | https://eprints.ums.edu.my/id/eprint/34153/1/FULL%20TEXT.pdf https://eprints.ums.edu.my/id/eprint/34153/2/ABSTRACT.pdf |
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| author | Xu, Ming-Ming Jumat Sulaiman Labiyana Hanif Ali |
| author_facet | Xu, Ming-Ming Jumat Sulaiman Labiyana Hanif Ali |
| author_sort | Xu, Ming-Ming |
| collection | UMS |
| description | The primary objective of this paper is to develop the Refinement of Successive Over-Relaxation (RSOR) method based on a three-point linear rational finite difference-quadrature discretization scheme for the numerical solution of second-order linear Fredholm integro-differential equation (FIDE). Besides, to illuminate the superior performance of the proposed method, some numerical examples are presented and solved by implementing three approaches which are the Gauss-Seidel (GS), the Successive Over-Relaxation (SOR) and the RSOR methods. Lastly, through the comparison of the results, it is verified that the RSOR method is more effective than the other two methods, especially when considering the aspects of the number of iterations and running time. |
| first_indexed | 2024-03-06T03:20:12Z |
| format | Article |
| id | ums.eprints-34153 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:20:12Z |
| publishDate | 2022 |
| publisher | Penerbit UPM |
| record_format | dspace |
| spelling | ums.eprints-341532022-09-27T02:19:13Z https://eprints.ums.edu.my/id/eprint/34153/ Refinement of SOR iterative method for the linear rational finite difference solution of second-order Fredholm Integro-differential equations Xu, Ming-Ming Jumat Sulaiman Labiyana Hanif Ali QA1-939 Mathematics The primary objective of this paper is to develop the Refinement of Successive Over-Relaxation (RSOR) method based on a three-point linear rational finite difference-quadrature discretization scheme for the numerical solution of second-order linear Fredholm integro-differential equation (FIDE). Besides, to illuminate the superior performance of the proposed method, some numerical examples are presented and solved by implementing three approaches which are the Gauss-Seidel (GS), the Successive Over-Relaxation (SOR) and the RSOR methods. Lastly, through the comparison of the results, it is verified that the RSOR method is more effective than the other two methods, especially when considering the aspects of the number of iterations and running time. Penerbit UPM 2022 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/34153/1/FULL%20TEXT.pdf text en https://eprints.ums.edu.my/id/eprint/34153/2/ABSTRACT.pdf Xu, Ming-Ming and Jumat Sulaiman and Labiyana Hanif Ali (2022) Refinement of SOR iterative method for the linear rational finite difference solution of second-order Fredholm Integro-differential equations. Malaysian Journal of Mathematical Sciences, 16. pp. 105-117. ISSN 1823-8343 (P-ISSN) , 2289-750X (E-ISSN) https://www.researchgate.net/profile/Elena-Gomez-4/publication/360516101_Refinement_of_SOR_Iterative_Method_for_the_Linear_Rational_Finite_Difference_Solution_of_Second-Order_Fredholm_Integro-Differential_Equations/links/627b9a9d973bbb29cc758a53/Refinement-of-SOR-Iterative-Method-for-the-Linear-Rational-Finite-Difference-Solution-of-Second-Order-Fredholm-Integro-Differential-Equations.pdf https://doi.org/10.1063/5.0075402 https://doi.org/10.1063/5.0075402 |
| spellingShingle | QA1-939 Mathematics Xu, Ming-Ming Jumat Sulaiman Labiyana Hanif Ali Refinement of SOR iterative method for the linear rational finite difference solution of second-order Fredholm Integro-differential equations |
| title | Refinement of SOR iterative method for the linear rational finite difference solution of second-order Fredholm Integro-differential equations |
| title_full | Refinement of SOR iterative method for the linear rational finite difference solution of second-order Fredholm Integro-differential equations |
| title_fullStr | Refinement of SOR iterative method for the linear rational finite difference solution of second-order Fredholm Integro-differential equations |
| title_full_unstemmed | Refinement of SOR iterative method for the linear rational finite difference solution of second-order Fredholm Integro-differential equations |
| title_short | Refinement of SOR iterative method for the linear rational finite difference solution of second-order Fredholm Integro-differential equations |
| title_sort | refinement of sor iterative method for the linear rational finite difference solution of second order fredholm integro differential equations |
| topic | QA1-939 Mathematics |
| url | https://eprints.ums.edu.my/id/eprint/34153/1/FULL%20TEXT.pdf https://eprints.ums.edu.my/id/eprint/34153/2/ABSTRACT.pdf |
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