The decomposition method for singularly perturbed boundary value problems with the local perturbation of the initial conditions. Equations with convective terms
type: Item
instance of: scholarly article
title: The decomposition method for singularly perturbed boundary value problems with the local perturbation of the initial conditions. Equations with convective terms
zbMATH Open document ID: 0904.65097
author: G. I. Shishkin
author: Irina V. Tselishcheva
published in: Russian Mathematics
publication date: 1998-10-18T00:00:00Z
review text: The Dirichlet problem for singularly perturbed parabolic equations in one space variable is considered. The initial condition has unit local perturbations of a finite amplitude on a narrow subdomain of width \(2\delta\) and the perturbation parameter \(\varepsilon^2\) is the coefficient of the highest derivative occurring. It is shown that there does not exist rectangular piecewise uniform grids for classical difference schemes, so that the schemes would converge uniformly in \(\delta\) and \(\varepsilon\). However, using the method of additive selective of singularities and mobile concentrating grids monotone finite difference schemes can be constructed.
Mathematics Subject Classification ID: 65M55
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1175138
zbMATH Keywords: singular perturbation
zbMATH Keywords: Shiskin meshes
zbMATH Keywords: convergence
zbMATH Keywords: decomposition method
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: parabolic equations
zbMATH Keywords: monotone finite difference schemes
reviewed by: Thomas Sonar
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1175138