Affiliation:
1. Auckland University of Technology
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.
Publisher
Trans Tech Publications, Ltd.
Reference18 articles.
1. Nayfeh, A.H.: Introduction to perturbation techniques. Wiley, New York (1981).
2. O'Malley, R.E.: Introduction to Singular Perturbation. Academic, New York (1974).
3. Ganji, D.D., Rajabi, A.: Assessment of homotopy–perturbation and perturbation methods in heat radiation equations. Int. Commun. Heat Mass Transfer 33, 391–400 (2006).
4. Liu, G.L.: New research directions in singular perturbation theory: artificial parameter approach and inverse-perturbation technique. Conference of 7th Modern Mathematics and Mechanics, Shanghai, p.47–53 (1997).
5. Liao, S.J.: An approximate solution technique not depending on small parameters: a special example. Int. J. Non-Linear Mech. 303, 371–380 (1995).