Higher-Order WHEP Solutions of Quadratic Nonlinear Stochastic Oscillatory Equation

HTML  XML Download Download as PDF (Size: 520KB)  PP. 57-69  
DOI: 10.4236/eng.2013.55A009    3,520 Downloads   5,305 Views  Citations

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.

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.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.