Stochastic Oscillators with Quadratic Nonlinearity Using WHEP and HPM Methods

Amnah S. Al-Johani

Department of Applied Mathematics, College of Science, Northern Borders University, Arar, Saudi Arabia&College of Home Economics, Northern Borders University, Arar, Saudi Arabia.

DOI: 10.4236/ajcm.2013.33027                

Abstract

In this paper, quadratic nonlinear oscillators under stochastic excitation are considered. The Wiener-Hermite expansion with perturbation (WHEP) method and the homotopy perturbation method (HPM) are used and compared. Different approximation orders are considered and statistical moments are computed in the two methods. The two methods show efficiency in estimating the stochastic response of the nonlinear differential equations.

Keywords

Nonlinear Stochastic Differential Equations; Wiener-Hermite Expansion; WHEP Technique; Homotopy Perturbation Method

Conflicts of Interest

The authors declare no conflicts of interest.

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