Approximate solutions to Van der Pol damped nonlinear oscillators by means of He's energy balance method

Abstract

In this article, He's energy balance method (EBM) is applied to solve Van der Pol damped nonlinear oscillators. Three examples of Van der Pol oscillators are presented and solved by this method to illustrate the effectiveness and convenience of the EBM. In this method, only one iteration leads to high accuracy of the solution. Comparisons are made between EBM results and exact solutions of the problems. The results show that the method can be easily extended to other nonlinear systems and can therefore be found widely applicable in engineering and other science.

Keywords:

• energy balance method
• Van der Pol equation
• nonconservative oscillatory system

2000 AMS Subject Classifications :

• 58D25
• 26A18
• 28DXX