Operator splitting for nonlinear reaction-diffusion systems with an entropic structure: Singular perturbation and order reduction
type: Item
instance of: scholarly article
title: Operator splitting for nonlinear reaction-diffusion systems with an entropic structure: Singular perturbation and order reduction
zbMATH Open document ID: 1060.65105
author: Stéphane Descombes
author: Marc Massot
published in: Numerische Mathematik
publication date: 2004-12-13T00:00:00Z
review text: The authors are interested in reaction-diffusion problems of the type \((U^\varepsilon \in\mathbb{R}^n)\): \[ \partial_tU^\varepsilon_x \cdot\bigl(B (U^\varepsilon) \partial_xU^\varepsilon\bigr)=F^\varepsilon,\quad x\in \mathbb{R}^d,\;t\geq 0 \] where \(B(U^\varepsilon)\), called diffusion matrix, is a tensor of order \(d\times d\times n\). The solution of this dynamical system is denoted by \(U^\varepsilon=T^t_\varepsilon U_0\), where \(U_0\) is the initial condition and \(\varepsilon>0\) is a small parameter. Then the singular perturbation results are presented followed by various operator splittings. The theoretical results are illustrated numerically together with the influence of the discretization on the results.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 2121822
zbMATH Keywords: singular perturbation
zbMATH Keywords: operator splittings
zbMATH Keywords: numerical examples
describes a project that uses: ODEPACK
MaRDI profile type: Publication
full work available at URL: s00211-003-0496-3
OpenAlex ID: W2061143699
DOI: 10.1007/S00211-003-0496-3
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description: scientific article; zbMATH DE number 2121822