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Embedded Runge-Kutta formulae with stable equilibrium states

Higham, D.J. and Hall, G. (1990) Embedded Runge-Kutta formulae with stable equilibrium states. Journal of Computational and Applied Mathematics, 29 (1). pp. 25-33. ISSN 0377-0427

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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.

Item type: Article
ID code: 210
Keywords: Runge-Kutta, embedded formulae, stability, stepsize selection, numerical mathematics, Mathematics, Computational Mathematics, Applied Mathematics
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Ms Sarah Scott
Date Deposited: 08 Mar 2006
Last modified: 10 Dec 2015 16:05

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