International Journal of Differential Equations
Volume 2011 (2011), Article ID 852919, 9 pages
http://dx.doi.org/10.1155/2011/852919
Research Article

Solutions of the Force-Free Duffing-van der Pol Oscillator Equation

Najeeb Alam Khan,1 Muhammad Jamil,2,3 Syed Anwar Ali,1 and Nadeem Alam Khan1

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 31 May 2011; Revised 5 August 2011; Accepted 22 August 2011

Academic Editor: Yuriy Rogovchenko

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

A new approximate method for solving the nonlinear Duffing-van der pol oscillator equation is proposed. The proposed scheme depends only on the two components of homotopy series, the Laplace transformation and, the Padé approximants. The proposed method introduces an alternative framework designed to overcome the difficulty of capturing the behavior of the solution and give a good approximation to the solution for a large time. The Runge-Kutta algorithm was used to solve the governing equation via numerical solution. Finally, to demonstrate the validity of the proposed method, the response of the oscillator, which was obtained from approximate solution, has been shown graphically and compared with that of numerical solution.