On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation
We develop the Newton-Kantorovich method to solve the system of 2×2 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 s...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/219616 |
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| _version_ | 1832552408672108544 |
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| author | Hameed Husam Hameed Z. K. Eshkuvatov Anvarjon Ahmedov N. M. A. Nik Long |
| author_facet | Hameed Husam Hameed Z. K. Eshkuvatov Anvarjon Ahmedov N. M. A. Nik Long |
| author_sort | Hameed Husam Hameed |
| collection | DOAJ |
| description | We develop the Newton-Kantorovich method to solve the system of 2×2 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. |
| format | Article |
| id | doaj-art-02f62987764e4fa6adf6195090d80397 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-02f62987764e4fa6adf6195090d803972025-02-03T05:58:39ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/219616219616On Newton-Kantorovich Method for Solving the Nonlinear Operator EquationHameed Husam Hameed0Z. K. Eshkuvatov1Anvarjon Ahmedov2N. M. A. Nik Long3Department of Mathematics, Faculty of Science, Universiti Putra Malaysia (UPM), Selangor, MalaysiaFaculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), Negeri Sembilan, MalaysiaInstitute for Mathematical Research, Universiti Putra Malaysia (UPM), Selangor, MalaysiaDepartment of Mathematics, Faculty of Science, Universiti Putra Malaysia (UPM), Selangor, MalaysiaWe develop the Newton-Kantorovich method to solve the system of 2×2 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.http://dx.doi.org/10.1155/2015/219616 |
| spellingShingle | Hameed Husam Hameed Z. K. Eshkuvatov Anvarjon Ahmedov N. M. A. Nik Long On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation Abstract and Applied Analysis |
| 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://dx.doi.org/10.1155/2015/219616 |
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