Solving Nonlinear Stochastic Diffusion Models with Nonlinear Losses Using the Homotopy Analysis Method

Aisha A. Fareed, Hanafy H. El-Zoheiry, Magdy A. El-Tawil, Mohammed A. El-Beltagy, Hany N. Hassan

Department of Basic Sciences, Engineering Faculty, Benha University, Benha, Egypt.
Department of Electrical & Computer Engineering, Engineering Faculty, Effat University, Jeddah, KSA.
Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Cairo, Egypt.

DOI: 10.4236/am.2014.51014                

Abstract

This paper deals with the construction of approximate series solutions of diffusion models with stochastic excitation and nonlinear losses using the homotopy analysis method (HAM). The mean, variance and other statistical properties of the stochastic solution are computed. The solution technique was applied successfully to the 1D and 2D diffusion models. The scheme shows importance of choice of convergence-control parameter to guarantee the convergence of the solutions of nonlinear differential Equations. The results are compared with the Wiener-Hermite expansion with perturbation (WHEP) technique and good agreements are obtained.

Keywords

HAM Technique; WHEP Technique; Stochastic PDEs; Diffusion Models

Conflicts of Interest

The authors declare no conflicts of interest.

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