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

Magdy A. El-Tawil, Amna S. Al-Jihany

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.

Keywords


Nonlinear stochastic differential equations; Wiener-Hermite expansion; WHEP technique; homotopy perturbation; Pickard approximations; perturbation; Adomian decompositions; mathematica

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