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Solving Nonlinear Stochastic Diffusion Models with Nonlinear Losses Using the Homotopy Analysis Method
Department of Basic Sciences, Engineering Faculty, Benha University, Benha, Egypt
Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Cairo, Egypt
Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Cairo, Egypt
Department of Electrical & Computer Engineering, Engineering Faculty, Effat University, Jeddah, KSA
Department of Basic Sciences, Engineering Faculty, Benha University, Benha, Egypt
- 1 Department of Basic Sciences, Engineering Faculty, Benha University, Benha, Egypt
- 2 Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Cairo, Egypt
- 3 Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Cairo, Egypt
- 4 Department of Electrical & Computer Engineering, Engineering Faculty, Effat University, Jeddah, KSA
- 5 Department of Basic Sciences, Engineering Faculty, Benha University, Benha, Egypt
Applied Mathematics·Volume 05 (2013)·Pages 115–127·Published 25 December 2013·DOI10.4236/am.2014.51014
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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 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 agreement s are obtained.
KeywordsHAM TechniqueWHEP TechniqueStochastic PDEsDiffusion Models
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