Asymptotic error expansions for stiff equations: Applications
type: Item
instance of: scholarly article
title: Asymptotic error expansions for stiff equations: Applications
zbMATH Open document ID: 0688.65057
DOI: 10.1007/BF02242919
author: Reinhard Frank
author: Gabriela Kirlinger
author: W. Auzinger
published in: Computing
publication date: 1990-01-01T00:00:00Z
review text: In various previous papers the authors have studied the structure of the global discretization error for: the implicit Euler method [SIAM J. Numer. Anal. 27, 67-104 (1990; reviewed above)], the implicit midpoint rule and the implicit trapezoidal rule [Numer. Math. 56, 469-499 (1989; Zbl 0684.65075) and Report Nr. 77/88, Inst. für Angewandte und Numerische Mathematik, TU Wien (1988)], all applied to a general class of nonlinear stiff initial value problems. In the present paper the last results, even the asymptotically incorrect ones, are proved to be useful for an analysis of two acceleration techniques: extrapolation, both in strongly and in mildly stiff cases, and defect correction. Numerical results are discussed.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65B05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4128328
zbMATH Keywords: asymptotic error expansion
zbMATH Keywords: global discretization error
zbMATH Keywords: implicit Euler method
zbMATH Keywords: implicit midpoint rule
zbMATH Keywords: implicit trapezoidal rule
zbMATH Keywords: nonlinear stiff initial value problems
zbMATH Keywords: acceleration techniques
zbMATH Keywords: extrapolation
zbMATH Keywords: defect correction
zbMATH Keywords: Numerical results
reviewed by: Antonio de Castro
MaRDI profile type: Publication
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cites work: Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case
cites work: Q3031843
cites work: A semi-implicit mid-point rule for stiff systems of ordinary differential equations
cites work: B-convergence properties of defect correction methods. I, II
cites work: Iterated defect correction for the efficient solution of stiff systems of ordinary differential equations
cites work: Extrapolation at stiff differential equations
full work available at URL: https://doi.org/10.1007/bf02242919
OpenAlex ID: W2013065
description: scientific article; zbMATH DE number 4128328