Numerical Simulation of Van der Pol Equation Using Multiple Scales Modified Lindstedt–Poincare Method

Abstract

In this paper, an efficient perturbation algorithm combining the method of Multiple Scales and Modified Lindstedt–Poincare Techniques is proposed to solve the equation of Van der Pol oscillator with very strong nonlinearity. This algorithm combines the advantages of both methods. Solution of Van der Pol equation by the Multiple Scales Modified Lindstedt–Poincare (MSMLP) method is compared with the Multiple Scales method and numerical solution using MATLAB 7.8. The convergence criterion for the solution by Multiple Scales and MSMLP methods is discussed and shown that Multiple Scales method fails the convergence criterion for large values of small parameter, while MSMLP method satisfies the convergence criterion for both small and large values. Numerical simulation has been performed in MATLAB 7.8 for different values of small parameter to prove the efficiency and accuracy of the proposed method.