Runge-Kutta defect control using Hermite-Birkhoff interpolation

D.J. Higham

Runge-Kutta defect control using Hermite-Birkhoff interpolation

D.J. Higham

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	991-999
Number of pages	8
Journal	SIAM Journal on Scientific Computing
Volume	12
Issue number	5
Publication status	Published - 1991

Keywords

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

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http://locus.siam.org/SISC/volume-12/art_0912053.html

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KW - residual

KW - backward error

KW - Hermite–Birkhofi interpolation

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