A. Nayfeh, “Problems in Perturbation,” John Wiley & Sons, New York, 1993.

has been cited by the following article:

• TITLE: Higher-Order WHEP Solutions of Quadratic Nonlinear Stochastic Oscillatory Equation

  AUTHORS: Mohamed A. El-Beltagy, Amnah S. Al-Johani

  KEYWORDS: Oscillatory Equation; Nonlinear Differential Equations; Stochastic Differential Equation; Wiener-Hermite Expansion; Perturbation Technique

  JOURNAL NAME: Engineering, Vol.5 No.5A, May 24, 2013

  ABSTRACT: This paper introduces higher-order solutions of the quadratic nonlinear stochastic oscillatory equation. Solutions with different orders and different number of corrections are obtained with the WHEP technique which uses the WienerHermite expansion and perturbation technique. The equivalent deterministic equations are derived for each order and correction. The solution ensemble average and variance are estimated and compared for different orders, different number of corrections and different strengths of the nonlinearity. The solutions are simulated using symbolic computation software such as Mathematica. The comparisons between different orders and different number of corrections show the importance of higher-order and higher corrected WHEP solutions for the nonlinear stochastic differential equations.