Analytical Technique for Solving Second Order Generalized Strongly Nonlinear Duffing Equation with Varying Coefficients in Presence of Small Damping

Abstract

In this thesis, we have extended He’s homotopy perturbation method for obtaining the approximate analytical solution of second order generalized strongly nonlinear Duffing equation with varying coefficients in presence of significant small damping based on the extended form of the Krylov-Bogoliubov-Mitropolskii (KBM) method. Accuracy and validity of the solutions obtained by the present method are compared with the corresponding numerical solutions obtained by the well-known fourth order Runge- Kutta method in graphically. The method has been illustrated by examples. In this study, the present technique gives acceptable results avoiding any numerical complexity. The results presented through figures show that the approximations are of extreme accuracy with significant damping. The proposed method is simple and suitable for solving the above mentioned nonlinear damped systems.