A Note on the Solutions of the Van der Pol and Duffing Equations Using a Linearisation Method

We present a novel application of the successive linearisation method to the classical Van der Pol and Duffing oscillator equations. By recasting the governing equations as nonlinear eigenvalue problems we obtain accurate values of the frequency and amplitude. We demonstrate that the proposed method...

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Bibliographic Details
Main Authors: Sandile S. Motsa, Precious Sibanda
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2012/693453
Description
Summary:We present a novel application of the successive linearisation method to the classical Van der Pol and Duffing oscillator equations. By recasting the governing equations as nonlinear eigenvalue problems we obtain accurate values of the frequency and amplitude. We demonstrate that the proposed method can be used to obtain the limit cycle and bifurcation diagrams of the governing equations. Comparison with exact and other results in the literature shows that the method is accurate and effective in finding solutions of nonlinear equations with oscillatory solutions, nonlinear eigenvalue problems, and other nonlinear problems with bifurcations.
ISSN:1024-123X
1563-5147