One dimensional nonlinear integral operator with Newton–Kantorovich method
The Newton–Kantorovich method (NKM) is widely used to find approximate solutions for nonlinear problems that occur in many fields of applied mathematics. This method linearizes the problems and then attempts to solve the linear problems by generating a sequence of functions. In this study, we have a...
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| Format: | Article |
| Language: | English |
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King Saud University
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/43324/1/One%20dimensional%20nonlinear%20integral%20operator%20with%20Newton%E2%80%93Kantorovich%20method.pdf |
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| author | Eshkuratov, Zainidin K. Hameed, Hameed Husam Nik Long, Nik Mohd Asri |
| author_facet | Eshkuratov, Zainidin K. Hameed, Hameed Husam Nik Long, Nik Mohd Asri |
| author_sort | Eshkuratov, Zainidin K. |
| collection | UPM |
| description | The Newton–Kantorovich method (NKM) is widely used to find approximate solutions for nonlinear problems that occur in many fields of applied mathematics. This method linearizes the problems and then attempts to solve the linear problems by generating a sequence of functions. In this study, we have applied NKM to Volterra-type nonlinear integral equations then the method of Nystrom type Gauss–Legendre quadrature formula (QF) was used to find the approximate solution of a linear Fredholm integral equation. New concept of determining the solution based on subcollocation points is proposed. The existence and uniqueness of the approximated method are proven. In addition, the convergence rate is established in Banach space. Finally illustrative examples are provided to validate the accuracy of the presented method. |
| first_indexed | 2024-03-06T08:55:20Z |
| format | Article |
| id | upm.eprints-43324 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:55:20Z |
| publishDate | 2016 |
| publisher | King Saud University |
| record_format | dspace |
| spelling | upm.eprints-433242016-05-18T04:46:26Z http://psasir.upm.edu.my/id/eprint/43324/ One dimensional nonlinear integral operator with Newton–Kantorovich method Eshkuratov, Zainidin K. Hameed, Hameed Husam Nik Long, Nik Mohd Asri The Newton–Kantorovich method (NKM) is widely used to find approximate solutions for nonlinear problems that occur in many fields of applied mathematics. This method linearizes the problems and then attempts to solve the linear problems by generating a sequence of functions. In this study, we have applied NKM to Volterra-type nonlinear integral equations then the method of Nystrom type Gauss–Legendre quadrature formula (QF) was used to find the approximate solution of a linear Fredholm integral equation. New concept of determining the solution based on subcollocation points is proposed. The existence and uniqueness of the approximated method are proven. In addition, the convergence rate is established in Banach space. Finally illustrative examples are provided to validate the accuracy of the presented method. King Saud University 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/43324/1/One%20dimensional%20nonlinear%20integral%20operator%20with%20Newton%E2%80%93Kantorovich%20method.pdf Eshkuratov, Zainidin K. and Hameed, Hameed Husam and Nik Long, Nik Mohd Asri (2016) One dimensional nonlinear integral operator with Newton–Kantorovich method. Journal of King Saud University - Science, 28 (2). pp. 172-177. ISSN 1018-3647; ESSN: 2213-686X http://www.sciencedirect.com/science/article/pii/S101836471500097X 10.1016/j.jksus.2015.10.004 |
| spellingShingle | Eshkuratov, Zainidin K. Hameed, Hameed Husam Nik Long, Nik Mohd Asri One dimensional nonlinear integral operator with Newton–Kantorovich method |
| title | One dimensional nonlinear integral operator with Newton–Kantorovich method |
| title_full | One dimensional nonlinear integral operator with Newton–Kantorovich method |
| title_fullStr | One dimensional nonlinear integral operator with Newton–Kantorovich method |
| title_full_unstemmed | One dimensional nonlinear integral operator with Newton–Kantorovich method |
| title_short | One dimensional nonlinear integral operator with Newton–Kantorovich method |
| title_sort | one dimensional nonlinear integral operator with newton kantorovich method |
| url | http://psasir.upm.edu.my/id/eprint/43324/1/One%20dimensional%20nonlinear%20integral%20operator%20with%20Newton%E2%80%93Kantorovich%20method.pdf |
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