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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 768963, 13 pages
Research Article

Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method

1Department of Mathematics, Science Faculty, Fırat University, 23119 Elazığ, Turkey
2Department of Mathematics, Education Faculty, Dicle University, 21280 Diyarbakır, Turkey
3Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA
4Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 18 December 2012; Accepted 5 March 2013

Academic Editor: Mustafa Bayram

Copyright © 2013 Mustafa Inc et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.