Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method-Reference-Cited by-同舟云学术

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

Published:2013 Issue: Volume:2013 Page:1-13
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Inc Mustafa¹^ORCID,Akgül Ali²³^ORCID,Kılıçman Adem⁴^ORCID

Affiliation:

1. Department of Mathematics, Science Faculty, Fırat University, 23119 Elazığ, Turkey

2. Department of Mathematics, Education Faculty, Dicle University, 21280 Diyarbakır, Turkey

3. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA

4. Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

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.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2013/768963.pdf

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