The homotopy analysis method and the Liénard equation

Abstract

In this article, Liénard equations are considered. The limit cycles of these systems are studied by applying the homotopy analysis method (HAM). The amplitude and frequency obtained with this methodology are in good agreement with those calculated by computational methods. This puts in evidence that HAM is a useful tool to solve nonlinear differential equations.

Keywords:

• Liénard equation
• homotopy analysis method
• limit cycles; the van der Pol oscillator
• perturbative techniques

2000 AMS Subject Classifications :

• 34C07
• 65L80

Acknowledgements

The authors would like to thank anonymous referees for valuable suggestions.

Additional information

Notes on contributors

S. Abbasbandy

Permanent address: Department of Mathematics, Imam Khomeini International University, Ghazvin 34149-16818, Iran.