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J. Sembera and M. Benes, “Nonlinear Galerkin Method for Reaction-Diffusion Systems Admitting Invariant Regions,” Journal of Computational and Applied Mathematics, Vol. 136, No. 1-2, 2001, pp. 163-176. doi:10.1016/S0377-0427(00)00582-3

has been cited by the following article:

• TITLE: Computational Studies of Reaction-Diffusion Systems by Nonlinear Galerkin Method

  AUTHORS: Miroslav Kolář

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

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.3 No.2, June 25, 2013

  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.