On the solution of stochastic oscillatory quadratic nonlinear equations using different techniques, a comparison study

Abstract

In this paper, nonlinear oscillators under quadratic
nonlinearity with stochastic inputs are considered.
Different methods are used to obtain first order approximations,
namely the WHEP technique, the perturbation method, the Pickard
approximations, the Adomian decompositions and the homotopy perturbation
method (HPM). Some statistical moments are computed for the different
methods using Mathematica 5. Comparisons are illustrated by figures
for different case-studies.