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.

Analytical Approximate Solution of Coupled Wave Equations with a Nonlinear Stiffness

“…The solution to the given nonlinear functional equation can be approximated by an infinite series solution of the linear and nonlinear terms, provided the nonlinear terms are represented by a sum of series of Adomian polynomials. 2,3,4 ADM has been successfully applied to various types of ordinary, 5,6,7 partial, 8,9,10,11,12 and delay differential equations 13 to develop closed-form approximate solutions.…”