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.
Highlights
It is well known that many problems often occur when one tries to approximate the complex dynamics of reaction-diffusion equations
This article deals with the computational study of the nonlinear Galerkin method, which is the extension of commonly known Faedo-Galerkin method
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
Summary
It is well known that many problems often occur when one tries to approximate the complex dynamics of reaction-diffusion equations. The error estimate of common methods grows exponentially in time. One possible approach to overcome this problem, known as the Nonlinear Galerkin method is suggested by Marion and Temam in [1]. It is discussed in [2] and [3]. In this paper we discuss this method and its properties, and apply it to the solution of particular reaction-diffusion model and perform a computational study when the method is compared with the commonly known Faedo-Galerkin method. We introduce the space H L2 a,b ; d as the Hilbert space with the scalar product d db
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