An Iteration Procedure with Application to Van der Pol Oscillator

作者：Herisanu Nicolae; Marinca Vasile^*

来源：International Journal of Nonlinear Sciences and Numerical Simulation, 2009, 10(3): 353-361.

DOI：10.1515/ijnsns.2009.10.3.353

• Non-linear equation
• iteration procedure
• resonance
• Van der Pol equation
• periodic solution

In this paper, a simple but effective iteration procedure to search the solution of the van der Pol equation is proposed. This procedure is a powerful tool for determination of periodic solution of a nonlinear equation of motion. The initial condition x(0) = 0 is often simplified to x(nh) = (0) = 0 (n=0, 1,2,...) and taken as an additional condition for the homogenous solution X(nh). The solutions obtained using the present conditions and corresponding iteration procedure are in good agreement with the numerical integration results obtained by a fourth order Runge-Kutta method, which shows the accuracy of the procedure.

• 出版日期2009-3