Highly continuous Runge-Kutta interpolants

D.J. Higham

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

To augment the discrete Runge-Kutta solutlon to the mitlal value problem, piecewlse Hermite interpolants have been used to provide a continuous approximation with a continuous first derivative We show that it M possible to construct mterpolants with arbltrardy many continuous derivatives which have the same asymptotic accuracy and basic cost as the Hermite interpol ants. We also show that the usual truncation coefficient analysis can be applied to these new interpolants, allowing their accuracy to be examined in more detad As an Illustration, we present some globally C2 interpolants for use with a popular 4th and 5th order Runge-Kutta pair of Dormand and Prince, and we compare them theoretically and numerically with existing interpolants.
LanguageEnglish
Pages368-386
Number of pages18
JournalACM Transactions on Mathematical Software
Volume17
Issue number3
DOIs
Publication statusPublished - Sep 1991

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Interpolants
Runge-Kutta
Derivatives
Hermite
Derivative
Truncation
Costs
Coefficient
Approximation

Keywords

  • performance
  • reliability
  • runge-kutta methods
  • numerical mathematics

Cite this

Higham, D.J. / Highly continuous Runge-Kutta interpolants. In: ACM Transactions on Mathematical Software. 1991 ; Vol. 17, No. 3. pp. 368-386.
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Highly continuous Runge-Kutta interpolants. / Higham, D.J.

In: ACM Transactions on Mathematical Software, Vol. 17, No. 3, 09.1991, p. 368-386.

Research output: Contribution to journalArticle

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