Abstract and Applied Analysis

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

Mustafa Inc, Ali Akgül, and Adem Kılıçman

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 768963, 13 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393448836

Digital Object Identifier
doi:10.1155/2013/768963

Mathematical Reviews number (MathSciNet)
MR3096813

Zentralblatt MATH identifier
07095346

Citation

Inc, Mustafa; Akgül, Ali; Kılıçman, Adem. Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 768963, 13 pages. doi:10.1155/2013/768963. https://projecteuclid.org/euclid.aaa/1393448836


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