A Simple Numerical Method For Van der Pol-Duffing Oscillator Equation

Abstract

The famous Van der Pol-Duffing oscillator is a typical nonlinear oscillator, its accurate analytical solution can not yet directly be got now. The segmenting recursion method was put forward in this paper, the oscillator equation was reasonably linearized within small segment, then the approximate analytical solutions within small segment were got, and the recursion formulas were obtained, finally all numerical solutions were got by the recursion formulas. The numerical solutions of several Van der Pol-Duffing oscillator equation were got by means of the segmenting recursion method, and the numerical solutions were compared with Runge-Kutta method or Gear linear multistep method. The comparative results show that the segmenting recursion method is very effective to solve Van der Pol-Duffing oscillator equation, not only method is simple, programming is easy, butresult is accurate, this method is a universal new method to solve similar oscillator.