Uniformly convergent difference schemes for a first boundary value problem for elliptic differential equations with a small parameter at the highest derivative
type: Item
instance of: scholarly article
title: Uniformly convergent difference schemes for a first boundary value problem for elliptic differential equations with a small parameter at the highest derivative
zbMATH Open document ID: 0633.65090
DOI: 10.1007/BF01895983
author: Biyue Liu
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1986-01-01T00:00:00Z
review text: The Dirichlet problem for the elliptic equation \[ \partial^ 2u/\partial x^ 2+\epsilon \partial^ 2u/\partial y^ 2+a\partial u/\partial x-b\partial u/\partial y-cu=f \] with a small parameter \(\epsilon >b\) is considered in the case of a region \(\Omega =\{(x,y)| \quad y_ 0\leq y\leq y^ 0\gamma_ 1(y)\leq x\leq \gamma_ 2(y)\}.\) A necessary condition for the uniform convergence of difference schemes is discussed and a special scheme with uniform convergence is suggested.
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4030887
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: small parameter
zbMATH Keywords: uniform convergence
zbMATH Keywords: difference schemes
reviewed by: Evgeniĭ Dyakonov
MaRDI profile type: Publication
cites work: Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
cites work: Q3909948
cites work: The parabolic equation as a limiting case of a certain elliptic equation
description: scientific article; zbMATH DE number 4030887