Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations
This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution 𝑢(𝑥) is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution 𝑢𝑛(𝑥)...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/839836 |
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| author | Omar Abu Arqub Mohammed Al-Smadi Shaher Momani |
| author_facet | Omar Abu Arqub Mohammed Al-Smadi Shaher Momani |
| author_sort | Omar Abu Arqub |
| collection | DOAJ |
| description | This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution 𝑢(𝑥) is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution 𝑢𝑛(𝑥) is obtained and it is proved to converge to the exact solution 𝑢(𝑥). Furthermore, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solution and its derivative will be applicable. Numerical examples are included to demonstrate the accuracy and applicability of the presented technique. The results reveal that the method is very effective and simple. |
| format | Article |
| id | doaj-art-088723a66a4f4b7d8f0a862bab4523e3 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-088723a66a4f4b7d8f0a862bab4523e32025-08-20T02:01:34ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/839836839836Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential EquationsOmar Abu Arqub0Mohammed Al-Smadi1Shaher Momani2Department of Mathematics, Al-Balqa Applied University, Salt 19117, JordanDepartment of Mathematics and Information Technology, Tafila Technical University, Tafila 66110, JordanDepartment of Mathematics, University of Jordan, Amman 11942, JordanThis paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution 𝑢(𝑥) is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution 𝑢𝑛(𝑥) is obtained and it is proved to converge to the exact solution 𝑢(𝑥). Furthermore, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solution and its derivative will be applicable. Numerical examples are included to demonstrate the accuracy and applicability of the presented technique. The results reveal that the method is very effective and simple.http://dx.doi.org/10.1155/2012/839836 |
| spellingShingle | Omar Abu Arqub Mohammed Al-Smadi Shaher Momani Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations Abstract and Applied Analysis |
| title | Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations |
| title_full | Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations |
| title_fullStr | Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations |
| title_full_unstemmed | Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations |
| title_short | Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations |
| title_sort | application of reproducing kernel method for solving nonlinear fredholm volterra integrodifferential equations |
| url | http://dx.doi.org/10.1155/2012/839836 |
| work_keys_str_mv | AT omarabuarqub applicationofreproducingkernelmethodforsolvingnonlinearfredholmvolterraintegrodifferentialequations AT mohammedalsmadi applicationofreproducingkernelmethodforsolvingnonlinearfredholmvolterraintegrodifferentialequations AT shahermomani applicationofreproducingkernelmethodforsolvingnonlinearfredholmvolterraintegrodifferentialequations |