An approximate solution of two dimensional nonlinear Volterra integral equation using Newton-Kantorovich method
This paper studies the method for establishing an approximate solution of nonlinear two dimensional Volterra integral equations (NLTD-VIE). The Newton-Kantorovich (NK) suppositions are employed to modify NLTD-VIE to the sequence of linear two dimensional Volterra integral equation (LTD-VIE). The pro...
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| Format: | Article |
| Language: | English |
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Faculty of Science, University of Malaya
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/51931/ http://psasir.upm.edu.my/id/eprint/51931/1/An%20approximate%20solution%20of%20two%20dimensional%20nonlinear%20Volterra%20integral%20equation%20using%20Newton-Kantorovich%20method.pdf |
| _version_ | 1848851967910084608 |
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| author | Hameed, Hameed Husam Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri |
| author_facet | Hameed, Hameed Husam Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri |
| author_sort | Hameed, Hameed Husam |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper studies the method for establishing an approximate solution of nonlinear two dimensional Volterra integral equations (NLTD-VIE). The Newton-Kantorovich (NK) suppositions are employed to modify NLTD-VIE to the sequence of linear two dimensional Volterra integral equation (LTD-VIE). The proper-ties of the two dimensional Gauss-Legenre (GL) quadrature fromula are used to abridge the sequence of LTD-VIE to the solution of the linear algebraic system. The existence and uniqueness of the approximate solution is demonstrated, and an illustrative example is provided to show the precision and authenticity of the method. |
| first_indexed | 2025-11-15T10:30:36Z |
| format | Article |
| id | upm-51931 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:30:36Z |
| publishDate | 2016 |
| publisher | Faculty of Science, University of Malaya |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-519312017-05-03T09:21:08Z http://psasir.upm.edu.my/id/eprint/51931/ An approximate solution of two dimensional nonlinear Volterra integral equation using Newton-Kantorovich method Hameed, Hameed Husam Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri This paper studies the method for establishing an approximate solution of nonlinear two dimensional Volterra integral equations (NLTD-VIE). The Newton-Kantorovich (NK) suppositions are employed to modify NLTD-VIE to the sequence of linear two dimensional Volterra integral equation (LTD-VIE). The proper-ties of the two dimensional Gauss-Legenre (GL) quadrature fromula are used to abridge the sequence of LTD-VIE to the solution of the linear algebraic system. The existence and uniqueness of the approximate solution is demonstrated, and an illustrative example is provided to show the precision and authenticity of the method. Faculty of Science, University of Malaya 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/51931/1/An%20approximate%20solution%20of%20two%20dimensional%20nonlinear%20Volterra%20integral%20equation%20using%20Newton-Kantorovich%20method.pdf Hameed, Hameed Husam and Eshkuvatov, Zainidin K. and Nik Long, Nik Mohd Asri (2016) An approximate solution of two dimensional nonlinear Volterra integral equation using Newton-Kantorovich method. Malaysian Journal of Science, 35 (1). pp. 37-43. ISSN 0126-7906 http://e-journal.um.edu.my/publish/MJS/1005-1203 |
| spellingShingle | Hameed, Hameed Husam Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri An approximate solution of two dimensional nonlinear Volterra integral equation using Newton-Kantorovich method |
| title | An approximate solution of two dimensional nonlinear Volterra integral equation using Newton-Kantorovich method |
| title_full | An approximate solution of two dimensional nonlinear Volterra integral equation using Newton-Kantorovich method |
| title_fullStr | An approximate solution of two dimensional nonlinear Volterra integral equation using Newton-Kantorovich method |
| title_full_unstemmed | An approximate solution of two dimensional nonlinear Volterra integral equation using Newton-Kantorovich method |
| title_short | An approximate solution of two dimensional nonlinear Volterra integral equation using Newton-Kantorovich method |
| title_sort | approximate solution of two dimensional nonlinear volterra integral equation using newton-kantorovich method |
| url | http://psasir.upm.edu.my/id/eprint/51931/ http://psasir.upm.edu.my/id/eprint/51931/ http://psasir.upm.edu.my/id/eprint/51931/1/An%20approximate%20solution%20of%20two%20dimensional%20nonlinear%20Volterra%20integral%20equation%20using%20Newton-Kantorovich%20method.pdf |