Analytical Solutions of Second Order Nonlinear Ordinary Differential Systems with high Order Nonlinearity

Abstract

Nonlinear oscillator models have been widely used in many areas of physics and engineering and are of significant importance in mechanical and structural dynamics for the comprehensive understanding and accurate prediction of motion. The aim of the present study is to solve the second order autonomous Nonlinear Differential Systems with strong and high ((9th)) order nonlinearity in presence of small damping by combing He’s homotopy perturbation and the extended form of the KBM methods. The results obtained by the presented method are compared with those solutions obtained by the fourth order Runge-Kutta method in graphically.