Runge-Kutta defect control using Hermite-Birkhoff interpolation

D.J. Higham

Research output: Contribution to journal › Article

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.
LanguageEnglish
Pages991-999
Number of pages8
JournalSIAM Journal on Scientific Computing
Volume12
Issue number5
Publication statusPublished - 1991

Fingerprint

Birkhoff Interpolation
Hermite Interpolation
Runge-Kutta
Interpolation
Defects
Runge-Kutta Schemes
Asymptotic analysis
Initial value problems
Asymptotic Analysis
Initial Value Problem
Numerical Solution
Alternatives

Keywords

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

Cite this

Higham, D.J. / Runge-Kutta defect control using Hermite-Birkhoff interpolation. In: SIAM Journal on Scientific Computing. 1991 ; Vol. 12, No. 5. pp. 991-999.
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Higham, DJ 1991, 'Runge-Kutta defect control using Hermite-Birkhoff interpolation' SIAM Journal on Scientific Computing, vol. 12, no. 5, pp. 991-999.

Runge-Kutta defect control using Hermite-Birkhoff interpolation. / Higham, D.J.

In: SIAM Journal on Scientific Computing, Vol. 12, No. 5, 1991, p. 991-999.

Research output: Contribution to journal › Article

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AB - 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.

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KW - defect

KW - residual

KW - backward error

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Higham DJ. Runge-Kutta defect control using Hermite-Birkhoff interpolation. SIAM Journal on Scientific Computing. 1991;12(5):991-999.

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