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

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.

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A. Al-Johani, "Stochastic Oscillators with Quadratic Nonlinearity Using WHEP and HPM Methods," *American Journal of Computational Mathematics*, Vol. 3 No. 3, 2013, pp. 185-194. doi: 10.4236/ajcm.2013.33027.

Conflicts of Interest

The authors declare no conflicts of interest.

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