Runge-Kutta defect control using Hermite-Birkhoff interpolation

D.J. Higham

Research output: Contribution to journalArticle

Abstract

Two techniques for reliably controlling the defect (residual) in the numerical solution of nonstifi initial value problems were given in [D. J. Higham, SIAM J. Numer. Anal., 26(1989), pp. 1175-1183]. This work describes an alternative approach based on Hermite-Birkhofi interpolation. The new approach has two main advantages-it is applicable to Runge-Kutta schemes of any order, and it gives rise to a defect of the optimum asymptotic order of accuracy. For a particular Runge-Kutta formula the asymptotic analysis is verified numerically.
Original languageEnglish
Pages (from-to)991-999
Number of pages8
JournalSIAM Journal on Scientific Computing
Volume12
Issue number5
Publication statusPublished - 1991

Keywords

  • Runge–Kutta
  • defect
  • residual
  • backward error
  • Hermite–Birkhofi interpolation
  • numerical mathematics

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