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He, J. H.: A coupling method of a homotopy technique and a perturbation technique for nonlinear problems. Int. J. Nonlinear Mech. 35, 37-43 (2000). doi:10.1016/S0020-7462(98)00085-7

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• TITLE: Solution of Stochastic Cubic and Quintic Nonlinear Diffusion Equation Using WHEP, Pickard and HPM Methods

  AUTHORS: Magdy A. El-Tawil, Aisha F. Fareed

  KEYWORDS: Stochastic Diffusion Equations, WHEP Technique, HPM Method

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.1 No.1, April 8, 2011

  ABSTRACT: In this paper, the cubic and quintic diffusion equation under stochastic non homogeneity is solved using Wiener- Hermite expansion and perturbation (WHEP) technique, Homotopy perturbation method (HPM) and Pickard approximation technique. The analytic solution of the linear case is obtained using Eigenfunction expansion .The Picard approximation method is used to introduce the first and second order approximate solution for the non linear case. The WHEP technique is also used to obtain approximate solution under different orders and different corrections. The Homotopy perturbation method (HPM) is also used to obtain some approximation orders for mean and variance. Using mathematica-5, the methods of solution are illustrated through figures, comparisons among different methods and some parametric studies.