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T. Imamura, W. Meecham and A. Siegel, “Symbolic Calculus of the Wiener Process and Wiener-Hermite Functionals,” Journal of Mathematical Physics, Vol. 6, No. 5, 1983, pp. 695-706. doi:10.1063/1.1704327

has been cited by the following article:

• TITLE: Stochastic Oscillators with Quadratic Nonlinearity Using WHEP and HPM Methods

  AUTHORS: Amnah S. Al-Johani

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

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.3 No.3, August 14, 2013

  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.