A study of B-convergence of linearly implicit Runge-Kutta methods
type: Item
instance of: scholarly article
title: A study of B-convergence of linearly implicit Runge-Kutta methods
zbMATH Open document ID: 0662.65071
DOI: 10.1007/BF02251252
author: K. Strehmel
author: R. Weiner
author: I. Dannehl
published in: Computing
publication date: 1988-01-01T00:00:00Z
review text: This paper analyses the B-convergence properties of linearly implicit Runge-Kutta methods when applied to stiff semi-linear problems. Sufficient conditions for a method to be B-consistent with a certain order are derived. A generalization of \textit{J. F. B. M. Kraaijevanger}'s technique [BIT 25, 652-666 (1985; Zbl 0584.65048)] for establishing the B-convergence of the implicit midpoint rule is used to demonstrate that for a certain singularly perturbed subclass of semi-linear problems the B-convergence order can be one more than the B-consistent order. Some numerical examples illustrate these points.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 4082876
zbMATH Keywords: B-convergence
zbMATH Keywords: linearly implicit Runge-Kutta methods
zbMATH Keywords: stiff semi-linear problems
zbMATH Keywords: implicit midpoint rule
zbMATH Keywords: B-consistent order
zbMATH Keywords: numerical examples
reviewed by: Kevin Burrage
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02251252
OpenAlex ID: W153782343
description: scientific article; zbMATH DE number 4082876