MATHEMATICAL MODELING OF QUINTIC DUFFING EQUATION AND NUMERICAL SIMULATION USING MULTIPLE SCALES MODIFIED LINDSTEDT–POINCARE METHOD

Abstract

A perturbation algorithm Multiple Scales Modified Lindstedt–Poincare (MSMLP), combination of method of Multiple Scales and modified Lindstedt–Poincare is proposed for the solution of Quintic Duffing equation which combines the advantages of both the methods. Solution obtained by the MSMLP method is compared with the Multiple Scales method and accurate closed form approximate solution of the Quintic Duffing equation. The proposed method produces better results for a wide range of amplitude values of oscillations and strong nonlinearities. Numerical simulation has been performed in MATHEMATICA 7.0.