Highly continuous Runge-Kutta interpolants

D.J. Higham

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)368-386
Number of pages18
JournalACM Transactions on Mathematical Software
Issue number3
Publication statusPublished - Sep 1991


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


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