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Higher-Order WHEP Solutions of Quadratic Nonlinear Stochastic Oscillatory Equation

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Author(s): Mohamed A. El-Beltagy | Amnah S. Al-Johani

Journal: Engineering
ISSN 1947-3931

Volume: 05;
Issue: 05;
Start page: 57;
Date: 2013;
Original page

Keywords: Oscillatory Equation | Nonlinear Differential Equations | Stochastic Differential Equation | Wiener-Hermite Expansion | Perturbation Technique

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.

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