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2011 Solutions of the Force-Free Duffing-van der Pol Oscillator Equation
Najeeb Alam Khan, Muhammad Jamil, Syed Anwar Ali, Nadeem Alam Khan
Int. J. Differ. Equ. 2011(SI2): 1-9 (2011). DOI: 10.1155/2011/852919


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.


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Najeeb Alam Khan. Muhammad Jamil. Syed Anwar Ali. Nadeem Alam Khan. "Solutions of the Force-Free Duffing-van der Pol Oscillator Equation." Int. J. Differ. Equ. 2011 (SI2) 1 - 9, 2011.


Received: 31 May 2011; Revised: 5 August 2011; Accepted: 22 August 2011; Published: 2011
First available in Project Euclid: 26 January 2017

zbMATH: 1239.34015
MathSciNet: MR2847594
Digital Object Identifier: 10.1155/2011/852919

Rights: Copyright © 2011 Hindawi


Vol.2011 • No. SI2 • 2011
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