Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type
We present an efficient iterative method for solving a class of nonlinear second-order Fredholm integrodifferential equations associated with different boundary conditions. A simple algorithm is given to obtain the approximate solutions for this type of equations based on the reproducing kernel spac...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/459509 |
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| _version_ | 1832566738877677568 |
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| author | Iryna Komashynska Mohammed AL-Smadi |
| author_facet | Iryna Komashynska Mohammed AL-Smadi |
| author_sort | Iryna Komashynska |
| collection | DOAJ |
| description | We present an efficient iterative method for solving a class of nonlinear second-order Fredholm integrodifferential equations associated with different boundary conditions. A simple algorithm is given to obtain the approximate solutions for this type of equations based on the reproducing kernel space method. The solution obtained by the method takes form of a convergent series with easily computable components. Furthermore, the error of the approximate solution is monotone decreasing with the increasing of nodal points. The reliability and efficiency of the proposed algorithm are demonstrated by some numerical experiments. |
| format | Article |
| id | doaj-art-1db7f690b8214e7e80778654efa0623a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1db7f690b8214e7e80778654efa0623a2025-02-03T01:03:20ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/459509459509Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm TypeIryna Komashynska0Mohammed AL-Smadi1Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanApplied Science Department, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanWe present an efficient iterative method for solving a class of nonlinear second-order Fredholm integrodifferential equations associated with different boundary conditions. A simple algorithm is given to obtain the approximate solutions for this type of equations based on the reproducing kernel space method. The solution obtained by the method takes form of a convergent series with easily computable components. Furthermore, the error of the approximate solution is monotone decreasing with the increasing of nodal points. The reliability and efficiency of the proposed algorithm are demonstrated by some numerical experiments.http://dx.doi.org/10.1155/2014/459509 |
| spellingShingle | Iryna Komashynska Mohammed AL-Smadi Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type Journal of Applied Mathematics |
| title | Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type |
| title_full | Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type |
| title_fullStr | Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type |
| title_full_unstemmed | Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type |
| title_short | Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type |
| title_sort | iterative reproducing kernel method for solving second order integrodifferential equations of fredholm type |
| url | http://dx.doi.org/10.1155/2014/459509 |
| work_keys_str_mv | AT irynakomashynska iterativereproducingkernelmethodforsolvingsecondorderintegrodifferentialequationsoffredholmtype AT mohammedalsmadi iterativereproducingkernelmethodforsolvingsecondorderintegrodifferentialequationsoffredholmtype |