Runge-Kutta pairs for periodic initial value problems
type: Item
instance of: scholarly article
title: Runge-Kutta pairs for periodic initial value problems
zbMATH Open document ID: 0787.65052
DOI: 10.1007/BF02243849
author: Ch. Tsitouras
author: S. N. Papakostas
author: George Papageorgiou
published in: Computing
publication date: 1994-05-24T00:00:00Z
review text: Pairs of different order (namely \(p\) and \(p-1\)) explicit \(s\)-stage Runge- Kutta formulae may be used to solve the initial value problem, the difference between the two solutions being used for local error approximation. In this paper, the authors discuss the phase-lag property of such methods when applied to problems with periodic solutions. They analyze two families, one of 5(4) pairs and the other of 6(5) pairs and from each select a pair with the highest possible order of phase-lag. New 5(4) pairs, based on pairs proposed by \textit{E. Fehlberg} [Computing 6, 61-71 (1970; Zbl 0217.530)] and by \textit{J. R. Dormand} and \textit{P. J. Prince} [J. Comput. Appl. Math. 6, 19-26 (1980; Zbl 0448.65045)], respectively, are of phase-lag order 8(4) and 8(6) and are not dissipative. The 6(5) pairs are of phase-lag order 10(6) and are dissipative (a dissipative scheme has non-vanishing imaginary stability interval). The paper concludes by demonstrating the generally improved performance of the new methods over other well known methods on some commonly utilized test problems whose solutions exhibit periodic behaviour.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 482259
zbMATH Keywords: explicit \(s\)-stage Runge-Kutta formulae
zbMATH Keywords: initial value problem
zbMATH Keywords: phase- lag
zbMATH Keywords: periodic solutions
zbMATH Keywords: stability interval
zbMATH Keywords: performance
reviewed by: Adrian Swift
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02243849
OpenAlex ID: W64179385
description: scientific article; zbMATH DE number 482259