## International Journal of Differential Equations

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

#### 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.

#### Article information

Source
Int. J. Differ. Equ., Volume 2011, Special Issue (2011), Article ID 852919, 9 pages.

Dates
Revised: 5 August 2011
Accepted: 22 August 2011
First available in Project Euclid: 26 January 2017

https://projecteuclid.org/euclid.ijde/1485399951

Digital Object Identifier
doi:10.1155/2011/852919

Mathematical Reviews number (MathSciNet)
MR2847594

Zentralblatt MATH identifier
1239.34015

#### Citation

Khan, Najeeb Alam; Jamil, Muhammad; Ali, Syed Anwar; Khan, Nadeem Alam. Solutions of the Force-Free Duffing-van der Pol Oscillator Equation. Int. J. Differ. Equ. 2011, Special Issue (2011), Article ID 852919, 9 pages. doi:10.1155/2011/852919. https://projecteuclid.org/euclid.ijde/1485399951

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