Numerical solution of a singularly perturbed elliptic-hyperbolic partial differential equation on a nonuniform discretization mesh
type: Item
instance of: scholarly article
title: Numerical solution of a singularly perturbed elliptic-hyperbolic partial differential equation on a nonuniform discretization mesh
zbMATH Open document ID: 0770.65064
DOI: 10.1007/BF02456147
author: Qiguang Wu
author: Xiaodi Sun
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1993-06-13T00:00:00Z
review text: The authors consider the upwind difference scheme for the following singular perturbation problem \[ \varepsilon(u_{xx}+u_{yy})+a(x,y)u_ x+b(x,y)u_ y-c(x,y)u=f(xy) \] \((x,y)\in \Omega=[0,1]\times [0,1]\) with the boundary condition \(u\mid_{\partial\Omega}=0\). On a special discretization mesh it is proved that the solution of the upwind difference scheme is first order convergent, uniformly in the small parameter \(\varepsilon\), to the solution of our problem. Numerical results are finally provided.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35M10
zbMATH DE Number: 177915
zbMATH Keywords: singular perturbation problem
zbMATH Keywords: upwind difference scheme
zbMATH Keywords: nonuniform discretization mesh
zbMATH Keywords: elliptic-hyperbolic
zbMATH Keywords: convergence
zbMATH Keywords: Numerical results
Wikidata QID: Q115392153
reviewed by: Laura Iulia Aniţa
MaRDI profile type: Publication
cites work: Q3727296
cites work: Q4206336
full work available at URL: https://doi.org/10.1007/bf02456147
OpenAlex ID: W2066766749
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description: scientific article; zbMATH DE number 177915