Higher-Order WHEP Solutions of Quadratic Nonlinear Stochastic Oscillatory Equation - Engineering

ENG > Vol.5 No.5, May 2013

Engineering

Volume 5, Issue 5 (May 2013)

ISSN Print: 1947-3931 ISSN Online: 1947-394X

Google-based Impact Factor: 0.66 Citations

Higher-Order WHEP Solutions of Quadratic Nonlinear Stochastic Oscillatory Equation ()

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Download as PDF (Size: 520KB) PP. 57-69

DOI: 10.4236/eng.2013.55A009 3,536 Downloads 5,349 Views Citations

Author(s)

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

Affiliation(s)

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.

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.

KEYWORDS

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

Share and Cite:

M. El-Beltagy and A. Al-Johani, "Higher-Order WHEP Solutions of Quadratic Nonlinear Stochastic Oscillatory Equation," Engineering, Vol. 5 No. 5A, 2013, pp. 57-69. doi: 10.4236/eng.2013.55A009.

Cited by

[1]	Solution of Nonlinear Stochastic Langevin's Equation Using WHEP, Pickard and HPM Methods
	Applied Mathematics, 2014

[2]	Numerical solution of stochastic nonlinear differential equations using wiener-hermite expansion
	Proceedings of the 11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM'13), 2013

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