On Newton-Kantorovich method for solving the nonlinear operator equation
We develop the Newton-Kantorovich method to solve the system of nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solutio...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/34733/ http://psasir.upm.edu.my/id/eprint/34733/1/On%20Newton-Kantorovich%20Method%20for%20Solving%20the%20Nonlinear.pdf |
| _version_ | 1848847856410034176 |
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| author | Hameed, Hameed Husam Eshkuvatov, Zainidin K. Ahmedov, Anvarjon Nik Long, Nik Mohd Asri |
| author_facet | Hameed, Hameed Husam Eshkuvatov, Zainidin K. Ahmedov, Anvarjon Nik Long, Nik Mohd Asri |
| author_sort | Hameed, Hameed Husam |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We develop the Newton-Kantorovich method to solve the system of nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method. |
| first_indexed | 2025-11-15T09:25:15Z |
| format | Article |
| id | upm-34733 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:25:15Z |
| publishDate | 2015 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-347332015-12-21T12:56:33Z http://psasir.upm.edu.my/id/eprint/34733/ On Newton-Kantorovich method for solving the nonlinear operator equation Hameed, Hameed Husam Eshkuvatov, Zainidin K. Ahmedov, Anvarjon Nik Long, Nik Mohd Asri We develop the Newton-Kantorovich method to solve the system of nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method. Hindawi Publishing Corporation 2015 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/34733/1/On%20Newton-Kantorovich%20Method%20for%20Solving%20the%20Nonlinear.pdf Hameed, Hameed Husam and Eshkuvatov, Zainidin K. and Ahmedov, Anvarjon and Nik Long, Nik Mohd Asri (2015) On Newton-Kantorovich method for solving the nonlinear operator equation. Abstract and Applied Analysis, 2015. art. no. 219616. pp. 1-12. ISSN 1085-3375; ESSN: 1687-0409 http://www.hindawi.com/journals/aaa/2015/219616/abs/ 10.1155/2015/219616 |
| spellingShingle | Hameed, Hameed Husam Eshkuvatov, Zainidin K. Ahmedov, Anvarjon Nik Long, Nik Mohd Asri On Newton-Kantorovich method for solving the nonlinear operator equation |
| title | On Newton-Kantorovich method for solving the nonlinear operator equation |
| title_full | On Newton-Kantorovich method for solving the nonlinear operator equation |
| title_fullStr | On Newton-Kantorovich method for solving the nonlinear operator equation |
| title_full_unstemmed | On Newton-Kantorovich method for solving the nonlinear operator equation |
| title_short | On Newton-Kantorovich method for solving the nonlinear operator equation |
| title_sort | on newton-kantorovich method for solving the nonlinear operator equation |
| url | http://psasir.upm.edu.my/id/eprint/34733/ http://psasir.upm.edu.my/id/eprint/34733/ http://psasir.upm.edu.my/id/eprint/34733/ http://psasir.upm.edu.my/id/eprint/34733/1/On%20Newton-Kantorovich%20Method%20for%20Solving%20the%20Nonlinear.pdf |