Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method
We investigate the effectiveness of reproducing kernel method (RKM) in solving partial differential equations. We propose a reproducing kernel method for solving the telegraph equation with initial and boundary conditions based on reproducing kernel theory. Its exact solution is represented in the f...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/768963 |
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| _version_ | 1849467857985863680 |
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| author | Mustafa Inc Ali Akgül Adem Kılıçman |
| author_facet | Mustafa Inc Ali Akgül Adem Kılıçman |
| author_sort | Mustafa Inc |
| collection | DOAJ |
| description | We investigate the effectiveness of reproducing kernel method (RKM) in solving partial differential equations. We propose a reproducing kernel method for solving the telegraph equation with initial and boundary conditions based on reproducing kernel theory. Its exact solution is represented in the form of a series in reproducing kernel Hilbert space. Some numerical examples are given in order to demonstrate the accuracy of this method. The results obtained from
this method are compared with the exact solutions and other methods. Results of numerical examples show that this method is simple, effective, and easy to use. |
| format | Article |
| id | doaj-art-e0bc4d3424d64995a0952d61fa8e1574 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e0bc4d3424d64995a0952d61fa8e15742025-08-20T03:26:00ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/768963768963Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space MethodMustafa Inc0Ali Akgül1Adem Kılıçman2Department of Mathematics, Science Faculty, Fırat University, 23119 Elazığ, TurkeyDepartment of Mathematics, Education Faculty, Dicle University, 21280 Diyarbakır, TurkeyDepartment of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaWe investigate the effectiveness of reproducing kernel method (RKM) in solving partial differential equations. We propose a reproducing kernel method for solving the telegraph equation with initial and boundary conditions based on reproducing kernel theory. Its exact solution is represented in the form of a series in reproducing kernel Hilbert space. Some numerical examples are given in order to demonstrate the accuracy of this method. The results obtained from this method are compared with the exact solutions and other methods. Results of numerical examples show that this method is simple, effective, and easy to use.http://dx.doi.org/10.1155/2013/768963 |
| spellingShingle | Mustafa Inc Ali Akgül Adem Kılıçman Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method Abstract and Applied Analysis |
| title | Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method |
| title_full | Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method |
| title_fullStr | Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method |
| title_full_unstemmed | Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method |
| title_short | Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method |
| title_sort | numerical solutions of the second order one dimensional telegraph equation based on reproducing kernel hilbert space method |
| url | http://dx.doi.org/10.1155/2013/768963 |
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