Analytical Solutions of Second Order Strongly Nonlinear Differential Systems with Slowly Varying Coefficients

Abstract

Considerable attention has been directed toward the study of strongly nonlinear differential systems. Nonlinear differential systems have been widely used in many areas of applied mathematics, physics, plasma and laser 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 develop an analytical technique for obtaining the approximate solutions of second order strongly nonlinear differential systems with slowly varying coefficients and higher order nonlinearity in presence of small damping based on the He’s homotopy perturbation method (HPM) and the extended form of the Krylov- Bogoliubov- Mitropolskii (KBM) method. Graphical representation of any physical system is important for its locations, amplitudes and phases. So the results obtained by the presented method are compared with those solutions obtained by the fourth order Runge-Kutta method in graphically.