S. J. Liao, “Notes on the Homotopy Analysis Method: Some Definitions and Theories,” Communications in Nonlinear Science Numerical Simulation, Vol. 14, No. 4, 2009, pp. 983-997.

has been cited by the following article:

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

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

  KEYWORDS: HAM Technique; WHEP Technique; Stochastic PDEs; Diffusion Models

  JOURNAL NAME: Applied Mathematics, Vol.5 No.1, January 10, 2014

  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.