Higher-Order WHEP Solutions of Quadratic Nonlinear Stochastic Oscillatory Equation

作     者：Mohamed A. El-Beltagy Amnah S. Al-Johani 

作者机构：Department of Applied Mathematics College of Science Northern Borders University Arar KSA College of Home Economics Northern Borders University Arar KSA Department of Engineering Mathematics & Physics Engineering Faculty Cairo University Giza Egypt 

出 版 物：《Engineering（科研）》 (工程（英文）（1947-3931）)

年 卷 期：2013年第5卷第5期

页      面：57-69页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Oscillatory Equation Nonlinear Differential Equations Stochastic Differential Equation Wiener-Hermite Expansion Perturbation Technique 

摘      要：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.