A general approach to counterexamples in numerical analysis
type: Item
instance of: scholarly article
title: A general approach to counterexamples in numerical analysis
zbMATH Open document ID: 0567.41025
DOI: 10.1007/BF01390126
author: W. Dickmeis
author: R. J. Nessel
author: Erich van Wickeren
published in: Numerische Mathematik
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/132900
review text: A general theorem is proved concerning the existence of functions which are smooth according to one generalized modulus of continuity and not smooth according to another. This theorem is then applied to several specific cases, including estimates for the trapezoid rule and Simpson's rule for quadrature. Examples concerning the rate of convergence of a method of lines for the heat equation are also presented.
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 3905165
zbMATH Keywords: modulus of continuity
zbMATH Keywords: trapezoid rule
zbMATH Keywords: Simpson's rule
zbMATH Keywords: rate of convergence
zbMATH Keywords: method of lines
zbMATH Keywords: heat equation
reviewed by: Gerald W. Hedstrom
MaRDI profile type: Publication
Wikidata QID: Q124851838
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OpenAlex ID: W2084662102
description: scientific article; zbMATH DE number 3905165