Half-sweep quadrature-difference schemes with iterative method in solving linear Fredholm integro-differential equations
In this paper, half-sweep iteration concept applied on quadrature-difference schemes with Gauss-Seidel (GS) iterative method in solving linear Fredholm integro-differential equations. The combinations of discretization schemes of repeated trapezoidal and Simpson's 1/3 with central difference sc...
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| Format: | Article |
| Language: | English English |
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Canadian Research & Development Center of Sciences and Cultures
2013
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| Online Access: | https://eprints.ums.edu.my/id/eprint/20303/1/Half%20sweep%20quadrature.pdf https://eprints.ums.edu.my/id/eprint/20303/7/Half-sweep%20quadrature-difference%20schemes%20with%20iterative%20method%20in%20solving%20linear%20Fredholm%20integro-differential%20equations.pdf |
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| author | E. Aruchunan Jumat Sulaiman |
| author_facet | E. Aruchunan Jumat Sulaiman |
| author_sort | E. Aruchunan |
| collection | UMS |
| description | In this paper, half-sweep iteration concept applied on quadrature-difference schemes with Gauss-Seidel (GS) iterative method in solving linear Fredholm integro-differential equations. The combinations of discretization schemes of repeated trapezoidal and Simpson's 1/3 with central difference schemes are analyzed. The formulation and the implementation of the proposed methods are explained in detail. In addition, several numerical experiments and computational complexity analysis were also carried out to validate the presentation of the schemes and methods. The findings show that, the HSGS iteration method is superior to the standard GS method. As well the high order quadrature scheme produced more accurate approximation solution compared to combination of repeated trapezoidal-central difference schemes. |
| first_indexed | 2024-03-06T02:57:28Z |
| format | Article |
| id | ums.eprints-20303 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T02:57:28Z |
| publishDate | 2013 |
| publisher | Canadian Research & Development Center of Sciences and Cultures |
| record_format | dspace |
| spelling | ums.eprints-203032021-09-29T04:30:05Z https://eprints.ums.edu.my/id/eprint/20303/ Half-sweep quadrature-difference schemes with iterative method in solving linear Fredholm integro-differential equations E. Aruchunan Jumat Sulaiman QA Mathematics In this paper, half-sweep iteration concept applied on quadrature-difference schemes with Gauss-Seidel (GS) iterative method in solving linear Fredholm integro-differential equations. The combinations of discretization schemes of repeated trapezoidal and Simpson's 1/3 with central difference schemes are analyzed. The formulation and the implementation of the proposed methods are explained in detail. In addition, several numerical experiments and computational complexity analysis were also carried out to validate the presentation of the schemes and methods. The findings show that, the HSGS iteration method is superior to the standard GS method. As well the high order quadrature scheme produced more accurate approximation solution compared to combination of repeated trapezoidal-central difference schemes. Canadian Research & Development Center of Sciences and Cultures 2013 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/20303/1/Half%20sweep%20quadrature.pdf text en https://eprints.ums.edu.my/id/eprint/20303/7/Half-sweep%20quadrature-difference%20schemes%20with%20iterative%20method%20in%20solving%20linear%20Fredholm%20integro-differential%20equations.pdf E. Aruchunan and Jumat Sulaiman (2013) Half-sweep quadrature-difference schemes with iterative method in solving linear Fredholm integro-differential equations. Progress in Applied Mathematics, 5 (1). pp. 11-21. ISSN 1925-2528 http://dx.doi.org/10.3968/j.pam.1925252820130501.2271 |
| spellingShingle | QA Mathematics E. Aruchunan Jumat Sulaiman Half-sweep quadrature-difference schemes with iterative method in solving linear Fredholm integro-differential equations |
| title | Half-sweep quadrature-difference schemes with iterative method in solving linear Fredholm integro-differential equations |
| title_full | Half-sweep quadrature-difference schemes with iterative method in solving linear Fredholm integro-differential equations |
| title_fullStr | Half-sweep quadrature-difference schemes with iterative method in solving linear Fredholm integro-differential equations |
| title_full_unstemmed | Half-sweep quadrature-difference schemes with iterative method in solving linear Fredholm integro-differential equations |
| title_short | Half-sweep quadrature-difference schemes with iterative method in solving linear Fredholm integro-differential equations |
| title_sort | half sweep quadrature difference schemes with iterative method in solving linear fredholm integro differential equations |
| topic | QA Mathematics |
| url | https://eprints.ums.edu.my/id/eprint/20303/1/Half%20sweep%20quadrature.pdf https://eprints.ums.edu.my/id/eprint/20303/7/Half-sweep%20quadrature-difference%20schemes%20with%20iterative%20method%20in%20solving%20linear%20Fredholm%20integro-differential%20equations.pdf |
| work_keys_str_mv | AT earuchunan halfsweepquadraturedifferenceschemeswithiterativemethodinsolvinglinearfredholmintegrodifferentialequations AT jumatsulaiman halfsweepquadraturedifferenceschemeswithiterativemethodinsolvinglinearfredholmintegrodifferentialequations |