Computational Studies of Reaction-Diffusion Systems by Nonlinear Galerkin Method

Miroslav Kolář

doi:10.4236/ajcm.2013.32022

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AJCM> Vol.3 No.2, June 2013

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Computational Studies of Reaction-Diffusion Systems by Nonlinear Galerkin Method

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DOI: 10.4236/ajcm.2013.32022 3,297 Downloads 5,828 Views

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Miroslav Kolář

Affiliation(s)

Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic.

ABSTRACT

This article deals with the computational study of the nonlinear Galerkin method, which is the extension of commonly known Faedo-Galerkin method. The weak formulation of the method is derived and applied to the particular Scott-Wang-Showalter reaction-diffusion model concerning the problem of combustion of hydrocarbon gases. The proof of convergence of the method based on the method of compactness is introduced. Presented results of numerical simulations are composed of the computational study, where the nonlinear Galerkin method and Faedo-Galerkin method are compared for the problem with analytical solution and the numerical results of the Scott-Wang-Showalter model in 1D.

KEYWORDS

Nonlinear Galerkin Method; Scott-Wang-Showalter Model; Compactness Method

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Kolář, "Computational Studies of Reaction-Diffusion Systems by Nonlinear Galerkin Method," American Journal of Computational Mathematics, Vol. 3 No. 2, 2013, pp. 137-146. doi: 10.4236/ajcm.2013.32022.

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