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

• 作者: Aisha A. Fareed Hanafy H. El-Zoheiry Hany N. Hassan Magdy A. El-Tawil Mohammed A. El-Beltagy
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: HAM TECHNIQUE WHEP TECHNIQUE STOCHASTIC PDES Diffusion Models
• 年，卷（期）: 2014,（1）
• 页码范围: 115-127
• 页数: 13页
• 分类号: O1

摘要

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.