Embedded Runge-Kutta formulae with stable equilibrium states

D.J. Higham; G. Hall

doi:10.1016/0377-0427(90)90192-3

Embedded Runge-Kutta formulae with stable equilibrium states

D.J. Higham, G. Hall

Mathematics And Statistics

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11 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 language	English
Pages (from-to)	25-33
Number of pages	8
Journal	Journal of Computational and Applied Mathematics
Volume	29
Issue number	1
DOIs	https://doi.org/10.1016/0377-0427(90)90192-3
Publication status	Published - 10 Jan 1990

Keywords

Runge-Kutta
embedded formulae
stability
stepsize selection
numerical mathematics

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10.1016/0377-0427(90)90192-3

Cite this

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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.",

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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

UR - http://dx.doi.org/10.1016/0377-0427(90)90192-3

U2 - 10.1016/0377-0427(90)90192-3

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

M3 - Article

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VL - 29

SP - 25

EP - 33

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

Embedded Runge-Kutta formulae with stable equilibrium states

Abstract

Keywords

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