Embedded Runge-Kutta formulae with stable equilibrium states

D.J. Higham, G. Hall

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The equilibrium theory of Hall and Higham (1988) can be used to determine whether a Runge-Kutta algorithm will perform smoothly when stability restricts the stepsize. In this paper we show that current high quality order 4, 5 pairs do not behave well in this respect, and we determine the extent to which the overall quality must be compromised in order for the equilibrium conditions to be satisfied. Three new formulae are presented and their properties are compared with those of existing formulae.
Original languageEnglish
Pages (from-to)25-33
Number of pages8
JournalJournal of Computational and Applied Mathematics
Volume29
Issue number1
DOIs
Publication statusPublished - 10 Jan 1990

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Runge-Kutta
Equilibrium State

Keywords

  • Runge-Kutta
  • embedded formulae
  • stability
  • stepsize selection
  • numerical mathematics

Cite this

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Embedded Runge-Kutta formulae with stable equilibrium states. / Higham, D.J.; Hall, G.

In: Journal of Computational and Applied Mathematics, Vol. 29, No. 1, 10.01.1990, p. 25-33.

Research output: Contribution to journalArticle

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AU - Hall, G.

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N2 - The equilibrium theory of Hall and Higham (1988) can be used to determine whether a Runge-Kutta algorithm will perform smoothly when stability restricts the stepsize. In this paper we show that current high quality order 4, 5 pairs do not behave well in this respect, and we determine the extent to which the overall quality must be compromised in order for the equilibrium conditions to be satisfied. Three new formulae are presented and their properties are compared with those of existing formulae.

AB - The equilibrium theory of Hall and Higham (1988) can be used to determine whether a Runge-Kutta algorithm will perform smoothly when stability restricts the stepsize. In this paper we show that current high quality order 4, 5 pairs do not behave well in this respect, and we determine the extent to which the overall quality must be compromised in order for the equilibrium conditions to be satisfied. Three new formulae are presented and their properties are compared with those of existing formulae.

KW - Runge-Kutta

KW - embedded formulae

KW - stability

KW - stepsize selection

KW - numerical mathematics

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DO - 10.1016/0377-0427(90)90192-3

M3 - Article

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

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