Matrix form of Legendre polynomials for solving linear integro-differential equations of high order
This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to trans...
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| Format: | Conference or Workshop Item |
| Language: | English |
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AIP Publishing
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57632/ http://psasir.upm.edu.my/id/eprint/57632/1/Matrix%20form%20of%20Legendre%20polynomials%20for%20solving%20linear%20integro-differential%20equations%20of%20high%20order.pdf |
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| author | Kammuji, M. Eshkuvatov, Zainidin K. Mohd Yunus, Arif Asraf |
| author_facet | Kammuji, M. Eshkuvatov, Zainidin K. Mohd Yunus, Arif Asraf |
| author_sort | Kammuji, M. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods. |
| first_indexed | 2025-11-15T10:53:42Z |
| format | Conference or Workshop Item |
| id | upm-57632 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:53:42Z |
| publishDate | 2016 |
| publisher | AIP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-576322017-10-24T08:15:40Z http://psasir.upm.edu.my/id/eprint/57632/ Matrix form of Legendre polynomials for solving linear integro-differential equations of high order Kammuji, M. Eshkuvatov, Zainidin K. Mohd Yunus, Arif Asraf This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods. AIP Publishing 2016 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57632/1/Matrix%20form%20of%20Legendre%20polynomials%20for%20solving%20linear%20integro-differential%20equations%20of%20high%20order.pdf Kammuji, M. and Eshkuvatov, Zainidin K. and Mohd Yunus, Arif Asraf (2016) Matrix form of Legendre polynomials for solving linear integro-differential equations of high order. In: 4th International Conference on Mathematical Sciences (ICMS4), 15-17 Nov. 2016, Putrajaya, Malaysia. (pp. 1-9). 10.1063/1.4980919 |
| spellingShingle | Kammuji, M. Eshkuvatov, Zainidin K. Mohd Yunus, Arif Asraf Matrix form of Legendre polynomials for solving linear integro-differential equations of high order |
| title | Matrix form of Legendre polynomials for solving linear integro-differential equations of high order |
| title_full | Matrix form of Legendre polynomials for solving linear integro-differential equations of high order |
| title_fullStr | Matrix form of Legendre polynomials for solving linear integro-differential equations of high order |
| title_full_unstemmed | Matrix form of Legendre polynomials for solving linear integro-differential equations of high order |
| title_short | Matrix form of Legendre polynomials for solving linear integro-differential equations of high order |
| title_sort | matrix form of legendre polynomials for solving linear integro-differential equations of high order |
| url | http://psasir.upm.edu.my/id/eprint/57632/ http://psasir.upm.edu.my/id/eprint/57632/ http://psasir.upm.edu.my/id/eprint/57632/1/Matrix%20form%20of%20Legendre%20polynomials%20for%20solving%20linear%20integro-differential%20equations%20of%20high%20order.pdf |