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Higher-Order WHEP Solutions of Quadratic Nonlinear Stochastic Oscillatory Equation
Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Giza, Egypt
Department of Applied Mathematics, College of Science, Northern Borders University, Arar, KSA；College of Home Economics, Northern Borders University, Arar, KSA
- 1 Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Giza, Egypt
- 2 Department of Applied Mathematics, College of Science, Northern Borders University, Arar, KSA；College of Home Economics, Northern Borders University, Arar, KSA
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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 Wiener Hermite 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 computa tion 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.
KeywordsOscillatory EquationNonlinear Differential EquationsStochastic Differential EquationWiener-Hermite ExpansionPerturbation Technique
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