International Journal of Differential Equations
- Int. J. Differ. Equ.
- Volume 2011, Special Issue (2011), Article ID 852919, 9 pages.
Solutions of the Force-Free Duffing-van der Pol Oscillator Equation
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.
Int. J. Differ. Equ., Volume 2011, Special Issue (2011), Article ID 852919, 9 pages.
Received: 31 May 2011
Revised: 5 August 2011
Accepted: 22 August 2011
First available in Project Euclid: 26 January 2017
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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