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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: Inc, Mustafa, Akgul, Ali, Kilicman, Adem
Format: Article
Language:English
Published: Hindawi Publishing Corporation 2013
Online Access:http://psasir.upm.edu.my/id/eprint/30199/1/30199.pdf
http://psasir.upm.edu.my/id/eprint/30199/
https://www.hindawi.com/journals/aaa/2013/768963/abs/
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spelling my.upm.eprints.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
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
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
author Inc, Mustafa
Akgul, Ali
Kilicman, Adem
spellingShingle Inc, Mustafa
Akgul, Ali
Kilicman, Adem
Numerical solutions of the second-order one-dimensional telegraph equation based on reproducing kernel Hilbert space method
author_facet Inc, Mustafa
Akgul, Ali
Kilicman, Adem
author_sort Inc, Mustafa
title 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_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_sort numerical solutions of the second-order one-dimensional telegraph equation based on reproducing kernel hilbert space method
publisher Hindawi Publishing Corporation
publishDate 2013
url http://psasir.upm.edu.my/id/eprint/30199/1/30199.pdf
http://psasir.upm.edu.my/id/eprint/30199/
https://www.hindawi.com/journals/aaa/2013/768963/abs/
_version_ 1643829987017490432
score 13.211869

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