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

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DOI: 10.4236/ojdm.2011.11002    4,311 Downloads   8,888 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. El-Tawil and A. Fareed, "Solution of Stochastic Cubic and Quintic Nonlinear Diffusion Equation Using WHEP, Pickard and HPM Methods," Open Journal of Discrete Mathematics, Vol. 1 No. 1, 2011, pp. 6-21. doi: 10.4236/ojdm.2011.11002.

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