Abstract
The WHEP algorithm showed a great efficiency in computing some statistical moments of the solution process for many perturbed stochastic differential equations. This technique has been greatly extended by the use of homotopy perturbation to yield what is called Homotopy WHEP in which the homotopy technique replaces the ordinary perturbation method which enables the application of the technique on non-perturbed problems. In this paper, the algorithm is applied on some nonlinear stochastic differential equations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
El-Tawil, M.: The application of WHEP technique on partial differential equations. Int. J. Different. Equ. Appl. 7(3), 325–337 (2003)
El-Tawil, M.: The Homotopy Wiener-Hermite expansion and perturbation technique (WHEP). In: Transactions on Computational Science I. LNCS, vol. 4750, pp. 159–180. Springer, New York (2008)
Saffman, P.: Application of Wiener-Hermite expansion to the diffusion of a passive scalar in a homogeneous turbulent flow. Phys. Fluids 12(9), 1786–1798 (1969)
Kambe, R., Doi, M.: Imamura and tsutomu, turbulent flows near flat plates. J. Phys. Soc. Jpn. 49(2), 763–778 (1980)
Jahedi, A., Ahmadi, G.: Application of Wiener-Hermite expansion to non-stationary random vibration of a Duffing oscillator. J. Appl. Mech. Trans. ASME 50(2), 436–442 (1983)
Eftimiu and Cornel: First-order Wiener-Hermite expansion in the electromagnetic scattering by conducting rough surfaces. Radio Sci. 23(5), 769–779 (1988)
Gawad, E., El-Tawil, M.: General stochastic oscillatory systems. Appl. Math. Model. 17(6), 329–335 (1993)
El-Tawil, M., Mahmoud, G.: The solvability of parametrically forced oscillators using WHEP technique. Mech. Mech. Eng. 3(2), 181–188 (1999)
He, J.H.: Homotopy perturbation technique. Comput. Methods Appl. Mech. Eng. 178, 257–292 (1999)
Liao, S.J.: The proposed homotopy analysis technique for the solution of nonlinear problems. PhD thesis, Shanghai Jiao, Tong University (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
El-Tawil, M.A. (2013). Homotopy WHEP Algorithm, Solving Stochastic Differential Equations. In: Stavrinides, S., Banerjee, S., Caglar, S., Ozer, M. (eds) Chaos and Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33914-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-33914-1_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33913-4
Online ISBN: 978-3-642-33914-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)