International Journal of Differential Equations
Volume 2011 (2011), Article ID 649748, 7 pages
http://dx.doi.org/10.1155/2011/649748
Research Article

Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with Discontinuity

Najeeb Alam Khan,1 Muhammad Jamil,2,3 and Asmat Ara1

1Department of Mathematics, University of Karachi, Karachi 75270, Pakistan
2Abdul Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
3Department of Mathematics, NED University of Engineering and Technology, Karachi 75270, Pakistan

Received 28 May 2011; Accepted 14 June 2011

Academic Editor: Leonid Berezansky

Copyright © 2011 Najeeb Alam Khan 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 applied a new approach to obtain natural frequency of the nonlinear oscillator with discontinuity. He's Hamiltonian approach is modified for nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(u). We employed this method for higher-order approximate solution of the nonlinear oscillator equation. This property is used to obtain approximate frequency-amplitude relationship of a nonlinear oscillator with high accuracy. Many numerical results are given to prove the efficiency of the suggested technique.