Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case
type: Item
instance of: scholarly article
title: Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case
zbMATH Open document ID: 0684.65075
DOI: 10.1007/BF01396649
published in: Numerische Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133408
review text: The structure of the global discretization error is studied for the implicit midpoint and trapezoidal rules, applied to nonlinear stiff initial value problems. In general, the global error contains rapidly oscillating terms of order \(h^ 2\). For special classes of stiff problems, it is shown that these terms also contain a factor of \(\epsilon\), where -1/\(\epsilon\) is the magnitude of the stiff eigenvalues, and thus that a ``full'' asymptotic error expansion exists in the case \(\epsilon \ll h\).
reviewed by: Michael Sever
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4121340
zbMATH Keywords: stiff systems
zbMATH Keywords: implicit midpoint rule
zbMATH Keywords: global discretization error
zbMATH Keywords: trapezoidal rules
zbMATH Keywords: nonlinear stiff initial value problems
zbMATH Keywords: asymptotic error expansion
author: W. Auzinger
author: Reinhard Frank
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4121340