Uniform convergent monotone iterates for semilinear singularly perturbed parabolic problems
type: Item
instance of: scholarly article
title: Uniform convergent monotone iterates for semilinear singularly perturbed parabolic problems
zbMATH Open document ID: 1218.65096
published in: Journal of Computational and Applied Mathematics
publication date: 2011-05-17T00:00:00Z
review text: The author constructs a nonlinear monotone iterative scheme for solving semilinear singularly perturbed parabolic problems of the form \(u_t-Lu+f(x,y,t,u)=0\) for \((x,y,t)\in\omega\times(0,T]\), with boundary conditions \(u(x,y,t)=g(x,y,t)\) on \((x,y,t)\in\partial\omega\times(0,T]\) and initial conditions \(u(x,y,0)=\psi(x,y)\) on \((x,y)\in\overline\omega\), where \(\omega\) is a connected bounded domain in \({\mathbb R}^2\) with boundary \(\partial\omega\). The operator \(L\) is given by \(Lu=\varepsilon(u_{xx}+u_{yy})+b_1(x,y,t)u_x+b_2(x,y,t)u_y\) where \(\varepsilon\) is a small positive parameter and \(b_1,b_2,f,g,\psi\) are smooth functions. The monotone scheme leads to the existence and uniqueness of the solution and is shown to be uniformly convergent. The scheme is applied to reaction-diffusion and convection-reaction-diffusion problems and numerical comparison is made with other schemes.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K58
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 5895481
zbMATH Keywords: semilinear parabolic problem
zbMATH Keywords: singular perturbation
zbMATH Keywords: monotone iterative method
zbMATH Keywords: uniform convergence
zbMATH Keywords: numerical examples
zbMATH Keywords: convection-reaction-diffusion problems
zbMATH Keywords: numerical comparison
author: Igor Boglaev
MaRDI profile type: Publication
full work available at URL: j.cam.2011.02.009
OpenAlex ID: W2021980454
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DOI: 10.1016/J.CAM.2011.02.009
description: scientific article; zbMATH DE number 5895481