Die maximale Konsistenzordnung von Differenzenapproximationen nichtnegativer Art
type: Item
instance of: scholarly article
title: Die maximale Konsistenzordnung von Differenzenapproximationen nichtnegativer Art
zbMATH Open document ID: 0536.65074
DOI: 10.1007/BF01400922
author: Harry Yserentant
published in: Numerische Mathematik
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/132865
review text: The differential operator \[ (Ly)(x)=- \sum^{N}_{i,j=1}a_{ij}(x)(D_ iD_ jy)(x)+\sum^{N}_{i=1}a_ i(x)(D_ iy)(x)+a(x)y(x),x\in {\mathbb{R}}^ n \] is discretized by a set of difference operators \((L_ hy)(x)=-h^{-2}a_ 0(x,h)y(x)-h^{- 2}\sum^{m}_{k=1}a_ k(x,h)y(x+c_ kh).\) If L is elliptic in \(x=x_ 0\) and if \(a_ k(x_ 0,h)\geq 0\), \(0<h\leq h_ 0\), \(k=1,...,m\), it is shown, that \(L_ h\) is at most consistent of order two to L.
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 3852360
zbMATH Keywords: maximal order of consistency
zbMATH Keywords: inverse monotone type
zbMATH Keywords: M-matrices
zbMATH Keywords: nonnegative difference approximation
MaRDI profile type: Publication
cites work: Q5593607
cites work: Discrete maximum principle for finite-difference operators
cites work: Die Mehrstellenformeln für den Laplace-Operator
OpenAlex ID: W13399424
description: scientific article; zbMATH DE number 3852360