Assessment of Perturbation and Homotopy-Perturbation Methods for Solving Nonlinear Oscillator Equations

Abstract:

In this paper, two modified perturbation methods, namely, artificial parameter method (APM) and homotopy perturbation method (HPM) have been successfully implemented to find the solution of van der Pol nonlinear oscillator equation. Different from classical perturbation method, APM and HPM do not require small parameter and therefore, obtained approximate solutions may be uniformly valid for both weak nonlinear systems and strong nonlinear systems. Comparison of the results obtained by the proposed methods reveals that APM and HPM are more effective compared to classical perturbation method and with only a few terms, approximate the exact solution with a fairly reasonable error.

• Periodical: Applied Mechanics and Materials (Volume 376)
• Pages: 207-215
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.376.207
• Online since: August 2013
• Authors: Maziar Ramezani, Thomas Rainer Neitzert
• Keywords: Artificial Parameter Method (APM), Homotopy Perturbation Method (HPM), Van Der Pol Oscillator

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