SOR iterative method for the linear rational finite difference solution of second-order Fredholm integro-differential equations
In this paper, a new three-point linear rational finite difference (3LRFD) formula is investigated, which is combined with the compound trapezoidal scheme to discretize the differential term and integral term of second-order linear Fredholm integro-differential equation (SOLFIDE) respectively, and t...
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| Format: | Proceedings |
| Language: | English English |
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Springer
2022
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| Online Access: | https://eprints.ums.edu.my/id/eprint/34252/2/SOR%20iterative%20method%20for%20the%20linear%20rational%20finite%20difference%20solution%20of%20second-order%20Fredholm%20integro-differential%20equations.ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/34252/1/SOR%20Iterative%20Method%20for%20the%20Linear%20Rational%20Finite%20Difference%20Solution%20of%20Second-Order%20Fredholm%20Integro-Differential%20Equations.pdf |
| _version_ | 1825715022250115072 |
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| author | Ming, Ming Xu Jumat Sulaiman Labiyana Hanif Ali |
| author_facet | Ming, Ming Xu Jumat Sulaiman Labiyana Hanif Ali |
| author_sort | Ming, Ming Xu |
| collection | UMS |
| description | In this paper, a new three-point linear rational finite difference (3LRFD) formula is investigated, which is combined with the compound trapezoidal scheme to discretize the differential term and integral term of second-order linear Fredholm integro-differential equation (SOLFIDE) respectively, and then the corresponding 3LRFD-quadrature approximation equation can be derived and generate the large and dense linear system. Additionally, the Successive Over-Relaxation method is implemented to solve the generated linear system and ultimately obtain the numerical solution of the SOLFIDE. To verify the effectiveness and accuracy of the proposed method, several numerical examples are considered and solved through the classical Gauss–Seidel method, which illustrates that the proposed method leads to a fewer number of iterations and faster execution time, and higher accuracy. |
| first_indexed | 2024-03-06T03:20:28Z |
| format | Proceedings |
| id | ums.eprints-34252 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:20:28Z |
| publishDate | 2022 |
| publisher | Springer |
| record_format | dspace |
| spelling | ums.eprints-342522022-09-27T04:31:20Z https://eprints.ums.edu.my/id/eprint/34252/ SOR iterative method for the linear rational finite difference solution of second-order Fredholm integro-differential equations Ming, Ming Xu Jumat Sulaiman Labiyana Hanif Ali QA299.6-433 Analysis In this paper, a new three-point linear rational finite difference (3LRFD) formula is investigated, which is combined with the compound trapezoidal scheme to discretize the differential term and integral term of second-order linear Fredholm integro-differential equation (SOLFIDE) respectively, and then the corresponding 3LRFD-quadrature approximation equation can be derived and generate the large and dense linear system. Additionally, the Successive Over-Relaxation method is implemented to solve the generated linear system and ultimately obtain the numerical solution of the SOLFIDE. To verify the effectiveness and accuracy of the proposed method, several numerical examples are considered and solved through the classical Gauss–Seidel method, which illustrates that the proposed method leads to a fewer number of iterations and faster execution time, and higher accuracy. Springer 2022-03-26 Proceedings PeerReviewed text en https://eprints.ums.edu.my/id/eprint/34252/2/SOR%20iterative%20method%20for%20the%20linear%20rational%20finite%20difference%20solution%20of%20second-order%20Fredholm%20integro-differential%20equations.ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/34252/1/SOR%20Iterative%20Method%20for%20the%20Linear%20Rational%20Finite%20Difference%20Solution%20of%20Second-Order%20Fredholm%20Integro-Differential%20Equations.pdf Ming, Ming Xu and Jumat Sulaiman and Labiyana Hanif Ali (2022) SOR iterative method for the linear rational finite difference solution of second-order Fredholm integro-differential equations. https://link.springer.com/chapter/10.1007/978-981-16-8515-6_28 |
| spellingShingle | QA299.6-433 Analysis Ming, Ming Xu Jumat Sulaiman Labiyana Hanif Ali SOR iterative method for the linear rational finite difference solution of second-order Fredholm integro-differential equations |
| title | SOR iterative method for the linear rational finite difference solution of second-order Fredholm integro-differential equations |
| title_full | SOR iterative method for the linear rational finite difference solution of second-order Fredholm integro-differential equations |
| title_fullStr | SOR iterative method for the linear rational finite difference solution of second-order Fredholm integro-differential equations |
| title_full_unstemmed | SOR iterative method for the linear rational finite difference solution of second-order Fredholm integro-differential equations |
| title_short | SOR iterative method for the linear rational finite difference solution of second-order Fredholm integro-differential equations |
| title_sort | sor iterative method for the linear rational finite difference solution of second order fredholm integro differential equations |
| topic | QA299.6-433 Analysis |
| url | https://eprints.ums.edu.my/id/eprint/34252/2/SOR%20iterative%20method%20for%20the%20linear%20rational%20finite%20difference%20solution%20of%20second-order%20Fredholm%20integro-differential%20equations.ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/34252/1/SOR%20Iterative%20Method%20for%20the%20Linear%20Rational%20Finite%20Difference%20Solution%20of%20Second-Order%20Fredholm%20Integro-Differential%20Equations.pdf |
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