Staff Members - Benha University
Solving Nonlinear Stochastic Diffusion Models with Nonlinear Losses Using the Homotopy Analysis Method
Applied mathematics • 2014
Publication Information
Authors
Aisha A. Fareed, H. H. El-Zoheiry, M. A. El-Tawil, M. A. El-Beltagy and Hany N. Hassan
Keywords
HAM Technique; WHEP Technique; Stochastic PDEs; Diffusion Models
Journal
Applied mathematics
Publisher
Not Available
Volume
5
Issue
1
Pages
115-127
publication.type
International
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
This paper deals with the construction of approximate series solutions of diffusion models with stochastic excita-
tion 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 ħ to guarantee
the convergence of the solutions of nonlinear differential Equations. The results are compared with the Wien-
er-Hermite expansion with perturbation (WHEP) technique and good agreements are obtained.
tion 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 ħ to guarantee
the convergence of the solutions of nonlinear differential Equations. The results are compared with the Wien-
er-Hermite expansion with perturbation (WHEP) technique and good agreements are obtained.