Analytical treatment for nonlinear oscillation equations and vibratory system of waves

Abstract

Analytical approximate solutions of Duffing and Van der Pol equations as well as the system of coupled Euler-Bernoulli beams and wave equations are under consideration. To this end, the Adomian Decomposition Method (ADM) and variational iteration method (VIM) have been employed to obtain analytical solutions to these differential equations. The results are compared with accurate numerical computations, which show that ADM is a high performance and accurate method to use for the analytical solution of nonlinear physical problems.