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

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  • Sandile S. Motsa
  • Precious Sibanda

Abstract

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.

Suggested Citation

  • Sandile S. Motsa & Precious Sibanda, 2012. "A Note on the Solutions of the Van der Pol and Duffing Equations Using a Linearisation Method," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-10, September.
    • Handle: RePEc:hin:jnlmpe:693453
    DOI: 10.1155/2012/693453
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    Cited by:

    1. Ghaleb, A.F. & Abou-Dina, M.S. & Moatimid, G.M. & Zekry, M.H., 2021. "Analytic approximate solutions of the cubic–quintic Duffing–van​ der Pol equation with two-external periodic forcing terms: Stability analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 129-151.

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