Grid approximations to singularly perturbed parabolic equations with turning points
type: Item
instance of: scholarly article
title: Grid approximations to singularly perturbed parabolic equations with turning points
zbMATH Open document ID: 0998.65085
DOI: 10.1023/A:1011978225750
author: G. I. Shishkin
published in: Differential Equations
publication date: 2002-11-24T00:00:00Z
review text: Solutions of a singularly perturbed boundary value problem have a rather complicated behaviour in a neighbourhood of boundary and internal layers. The author considers a class of singularly perturbed parabolic equations with convective terms on a closed interval. The behaviour of the solution in a neighbourhood of the boundary \(x=0\) and the existence of a boundary layer as well as its decay character away from the boundary is determined by the sign of a function appearing in the equations under consideration. For this class of problems a uniformly convergent finite-difference scheme is constructed making use of the method of condensing grids in a neighbourhood of the boundary layers and the singularity of the solution.
reviewed by: Zbigniew Dżygadło
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 1758780
zbMATH Keywords: turning points
zbMATH Keywords: singular perturbation
zbMATH Keywords: convergence
zbMATH Keywords: parabolic equations
zbMATH Keywords: boundary layer
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1758780