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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30199/ http://psasir.upm.edu.my/id/eprint/30199/1/30199.pdf |
| _version_ | 1848846609647927296 |
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| author | Inc, Mustafa Akgul, Ali Kilicman, Adem |
| author_facet | Inc, Mustafa Akgul, Ali Kilicman, Adem |
| author_sort | Inc, Mustafa |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T09:05:26Z |
| format | Article |
| id | upm-30199 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:05:26Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-301992017-10-19T08:51:00Z http://psasir.upm.edu.my/id/eprint/30199/ Numerical solutions of the second-order one-dimensional telegraph equation based on reproducing kernel Hilbert space method Inc, Mustafa Akgul, Ali Kilicman, Adem 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. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30199/1/30199.pdf Inc, Mustafa and Akgul, Ali and Kilicman, Adem (2013) Numerical solutions of the second-order one-dimensional telegraph equation based on reproducing kernel Hilbert space method. Abstract and Applied Analysis, 2013. art. no. 768963. pp. 1-13. ISSN 1085-3375; ESSN: 1687-0409 https://www.hindawi.com/journals/aaa/2013/768963/abs/ 10.1155/2013/768963 |
| spellingShingle | Inc, Mustafa Akgul, Ali Kilicman, Adem Numerical solutions of the second-order one-dimensional telegraph equation based on reproducing kernel Hilbert space method |
| 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://psasir.upm.edu.my/id/eprint/30199/ http://psasir.upm.edu.my/id/eprint/30199/ http://psasir.upm.edu.my/id/eprint/30199/ http://psasir.upm.edu.my/id/eprint/30199/1/30199.pdf |