Abstract and Applied Analysis
Volume 2013 (2013), Article ID 578942, 11 pages
http://dx.doi.org/10.1155/2013/578942
Research Article

A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method

Mustafa Inc,1 Ali Akgül,2 and Adem Kiliçman3

1Department of Mathematics, Science Faculty, Firat University, 23119 Elaziğ, Turkey
2Department of Mathematics, Education Faculty, Dicle University, 21280 Diyarbakır, Turkey
3Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM), Selangor, 43400 Serdang, Malaysia

Received 19 September 2012; Revised 17 December 2012; Accepted 23 December 2012

Academic Editor: Lan Xu

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.

Abstract

We propose a reproducing kernel method for solving the KdV equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples have also been studied to demonstrate the accuracy of the present method. Results of numerical examples show that the presented method is effective.