Rational finite difference solution of first-order fredholm integro-differential equations via SOR iteration
The linear rational finite difference method (LRFD) is becomingmore and more popular recently due to its excellent stability properties and convergence rate, especially when we are approximating the derivative of some points near the end of the interval. The main intention of this paper is to combin...
| Main Authors: | , , |
|---|---|
| Format: | Conference or Workshop Item |
| Language: | English English |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://eprints.ums.edu.my/id/eprint/30186/5/Rational%20finite%20difference%20solution%20of%20first-order%20fredholm%20integro-differential%20equations%20via%20SOR%20iteration-%20Abstract.pdf https://eprints.ums.edu.my/id/eprint/30186/2/Rational%20Finite%20Difference%20Solution%20of%20First-Order%20Fredholm%20Integro-differential%20Equations%20via%20SOR%20Iteration.pdf |
| _version_ | 1825714310790250496 |
|---|---|
| author | M.M. Xu Jumat Sulaiman Labiyana Hanif Ali |
| author_facet | M.M. Xu Jumat Sulaiman Labiyana Hanif Ali |
| author_sort | M.M. Xu |
| collection | UMS |
| description | The linear rational finite difference method (LRFD) is becomingmore and more popular recently due to its excellent stability properties and convergence rate, especially when we are approximating the derivative of some points near the end of the interval. The main intention of this paper is to combine the 3-point linear rational finite difference (3LRFD) method with the composite trapezoidal (CT) quadrature formula to discretize the first-order linear integro-differential equation and produce dense linear systems. Furthermore, the numerical solution of the integrodifferential equation is obtained by implementing the Successive Over-Relaxation (SOR) method. At the same time, the classical Gauss–Seidel (GS) method is also introduced as the control condition. In the end, through several numerical examples, the number of iterations, the execution time and the maximum absolute error are compared, which fully illustrated the superiority of SOR method over GS method in solving large dense linear system generated by the CT-3LRFD formula. |
| first_indexed | 2024-03-06T03:09:55Z |
| format | Conference or Workshop Item |
| id | ums.eprints-30186 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:09:55Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ums.eprints-301862021-07-31T16:32:43Z https://eprints.ums.edu.my/id/eprint/30186/ Rational finite difference solution of first-order fredholm integro-differential equations via SOR iteration M.M. Xu Jumat Sulaiman Labiyana Hanif Ali Q Science (General) QA Mathematics The linear rational finite difference method (LRFD) is becomingmore and more popular recently due to its excellent stability properties and convergence rate, especially when we are approximating the derivative of some points near the end of the interval. The main intention of this paper is to combine the 3-point linear rational finite difference (3LRFD) method with the composite trapezoidal (CT) quadrature formula to discretize the first-order linear integro-differential equation and produce dense linear systems. Furthermore, the numerical solution of the integrodifferential equation is obtained by implementing the Successive Over-Relaxation (SOR) method. At the same time, the classical Gauss–Seidel (GS) method is also introduced as the control condition. In the end, through several numerical examples, the number of iterations, the execution time and the maximum absolute error are compared, which fully illustrated the superiority of SOR method over GS method in solving large dense linear system generated by the CT-3LRFD formula. 2021-03-16 Conference or Workshop Item PeerReviewed text en https://eprints.ums.edu.my/id/eprint/30186/5/Rational%20finite%20difference%20solution%20of%20first-order%20fredholm%20integro-differential%20equations%20via%20SOR%20iteration-%20Abstract.pdf text en https://eprints.ums.edu.my/id/eprint/30186/2/Rational%20Finite%20Difference%20Solution%20of%20First-Order%20Fredholm%20Integro-differential%20Equations%20via%20SOR%20Iteration.pdf M.M. Xu and Jumat Sulaiman and Labiyana Hanif Ali (2021) Rational finite difference solution of first-order fredholm integro-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_38 |
| spellingShingle | Q Science (General) QA Mathematics M.M. Xu Jumat Sulaiman Labiyana Hanif Ali Rational finite difference solution of first-order fredholm integro-differential equations via SOR iteration |
| title | Rational finite difference solution of first-order fredholm integro-differential equations via SOR iteration |
| title_full | Rational finite difference solution of first-order fredholm integro-differential equations via SOR iteration |
| title_fullStr | Rational finite difference solution of first-order fredholm integro-differential equations via SOR iteration |
| title_full_unstemmed | Rational finite difference solution of first-order fredholm integro-differential equations via SOR iteration |
| title_short | Rational finite difference solution of first-order fredholm integro-differential equations via SOR iteration |
| title_sort | rational finite difference solution of first order fredholm integro differential equations via sor iteration |
| topic | Q Science (General) QA Mathematics |
| url | https://eprints.ums.edu.my/id/eprint/30186/5/Rational%20finite%20difference%20solution%20of%20first-order%20fredholm%20integro-differential%20equations%20via%20SOR%20iteration-%20Abstract.pdf https://eprints.ums.edu.my/id/eprint/30186/2/Rational%20Finite%20Difference%20Solution%20of%20First-Order%20Fredholm%20Integro-differential%20Equations%20via%20SOR%20Iteration.pdf |
| work_keys_str_mv | AT mmxu rationalfinitedifferencesolutionoffirstorderfredholmintegrodifferentialequationsviasoriteration AT jumatsulaiman rationalfinitedifferencesolutionoffirstorderfredholmintegrodifferentialequationsviasoriteration AT labiyanahanifali rationalfinitedifferencesolutionoffirstorderfredholmintegrodifferentialequationsviasoriteration |