Analytical solution for Van der Pol–Duffing oscillators

In this paper, the problem of single-well, double-well and double-hump Van der Pol–Duffing oscillator is studied. Governing equation is solved analytically using a new kind of analytic technique for nonlinear problems namely the “Homotopy Analysis Method” (HAM), for the first time. Present solution...

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Bibliographic Details
Published in:	Chaos, solitons and fractals Vol. 42; no. 5; pp. 2660 - 2666
Main Authors:	Kimiaeifar, A., Saidi, A.R., Bagheri, G.H., Rahimpour, M., Domairry, D.G.
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 15-12-2009
Subjects:	Fractal analysis Ham Mathematical analysis Mathematical models Nonlinearity Oscillators Solitons
Online Access:	Get full text
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Summary:	In this paper, the problem of single-well, double-well and double-hump Van der Pol–Duffing oscillator is studied. Governing equation is solved analytically using a new kind of analytic technique for nonlinear problems namely the “Homotopy Analysis Method” (HAM), for the first time. Present solution gives an expression which can be used in wide range of time for all domain of response. Comparisons of the obtained solutions with numerical results show that this method is effective and convenient for solving this problem. This method is a capable tool for solving this kind of nonlinear problems.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0960-0779 1873-2887
DOI:	10.1016/j.chaos.2009.03.145