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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 5 > No. 1


Homotopy Analysis Wiener-Hermite Expansion Method for Solving Stochastic Differential Equation

PP: 13-26
Aisha F. Fareed, Magdy A. El-Tawil, Hany N. Hassan,
This paper introduces a new technique called Homotopy analysis Wiener Hermite expansion (HAM-WHE) which considered as an extension to Wiener Hermite expansion linked with perturbation technique WHEP. The WHEP technique uses the Wiener Hermite expansion and perturbation technique to solve a class of nonlinear partial differential equations with a perturbed nonlinearity. The homotopy perturbation method (HPM) was used instead of the conventional perturbation methods which generalizes the WHEP technique such that it can be applied to stochastic differential equations without the necessary of presence of the small parameter. For more generalizing, the homotopy analysis method (HAM) is used instead of HPM; since HAM contains the control parameter to guarantee the convergence of the solution and HPM is only a special case of HAM obtained at h = −1 .The proposed technique is applied on stochastic quadratic nonlinear diffusion problem to obtain some approximation orders of mean and variance with making comparisons with HAM and homotopy-WHE to testify the method of analysis using symbolic computation software Mathematica. The current work extends the use of WHEP for solving stochastic nonlinear differential equations.

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