Global error estimation with Runge-Kutta triples
type: Item
instance of: scholarly article
title: Global error estimation with Runge-Kutta triples
zbMATH Open document ID: 0683.65054
DOI: 10.1016/0898-1221(89)90181-8
author: J. R. Dormand
author: M. A. Lockyer
author: N. E. McGorrigan
author: P. J. Prince
publication date: 1989-01-01T00:00:00Z
review text: For the system: \(y'(x)=f[y(x)],\quad y(x_ 0)=y_ 0,\) the Zadunaisky technique for global error estimation of an embedded Runge-Kutta formula consists on calculating the error obtained with the same formula in a neighbouring problem with known solution; for example: \(y'_ h(x)=f_ h[y_ h(x)]=f[y_ h(x)]+d_ h(x),\quad y_ h(x_ 0)=y(x_ 0)=P(x_ 0);\quad d_ h(x)=P'(x)-f[P(x)]\) whose solution is \(y_ h(x)=P(x)\), [see: the first and the fourth author, IMA J. Numer. Anal. 5, 481-497 (1985; Zbl 0606.65048)]. The novelty of the present paper is that P(x) is formed using a triple Runge-Kutta formula [see: same authors, Comput. Math. Appl., Part A 12, 1007-1017 (1986; Zbl 0618.65059)] which allows the application of the estimation process at each integration step and not after a block of m steps. Some formulae, numerical tests and references are included.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4119521
zbMATH Keywords: numerical examples
zbMATH Keywords: Zadunaisky technique
zbMATH Keywords: global error estimation
zbMATH Keywords: embedded Runge-Kutta formula
zbMATH Keywords: triple Runge-Kutta formula
reviewed by: Antonio de Castro
MaRDI profile type: Publication
full work available at URL: 0898-1221(89)90181-8
OpenAlex ID: W1985921719
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4119521