Error estimation for Nordsieck methods

J. C. Butcher; Zdzislaw Jackiewicz

doi:10.1023/A:1021152005287

Error estimation for Nordsieck methods

J. C. Butcher, Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

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

15 Scopus citations

Abstract

The local discretization errors of general linear methods depend on the sequence of all stepsize ratios and the derivation of the exact formulas for the corresponding error estimates does not seem to be practical. In this paper we will describe an approach in which the estimates of local discretization errors are evaluated numerically as the computation proceeds from step to step.

Original language	English (US)
Pages (from-to)	75-85
Number of pages	11
Journal	Numerical Algorithms
Volume	31
Issue number	1-4
DOIs	https://doi.org/10.1023/A:1021152005287
State	Published - 2002

Keywords

Error estimation
General linear methods
Nordsieck methods
Step changing strategy

ASJC Scopus subject areas

Applied Mathematics

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title = "Error estimation for Nordsieck methods",

abstract = "The local discretization errors of general linear methods depend on the sequence of all stepsize ratios and the derivation of the exact formulas for the corresponding error estimates does not seem to be practical. In this paper we will describe an approach in which the estimates of local discretization errors are evaluated numerically as the computation proceeds from step to step.",

keywords = "Error estimation, General linear methods, Nordsieck methods, Step changing strategy",

author = "Butcher, {J. C.} and Zdzislaw Jackiewicz",

note = "Funding Information: ∗The work of this author was assisted by the Marsden Fund of New Zealand. ∗∗The work of this author was partially supported by the National Science NSF DMS-9971164.",

year = "2002",

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language = "English (US)",

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journal = "Numerical Algorithms",

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T1 - Error estimation for Nordsieck methods

AU - Butcher, J. C.

AU - Jackiewicz, Zdzislaw

N1 - Funding Information: ∗The work of this author was assisted by the Marsden Fund of New Zealand. ∗∗The work of this author was partially supported by the National Science NSF DMS-9971164.

PY - 2002

Y1 - 2002

N2 - The local discretization errors of general linear methods depend on the sequence of all stepsize ratios and the derivation of the exact formulas for the corresponding error estimates does not seem to be practical. In this paper we will describe an approach in which the estimates of local discretization errors are evaluated numerically as the computation proceeds from step to step.

AB - The local discretization errors of general linear methods depend on the sequence of all stepsize ratios and the derivation of the exact formulas for the corresponding error estimates does not seem to be practical. In this paper we will describe an approach in which the estimates of local discretization errors are evaluated numerically as the computation proceeds from step to step.

KW - Error estimation

KW - General linear methods

KW - Nordsieck methods

KW - Step changing strategy

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JF - Numerical Algorithms

IS - 1-4

ER -

Error estimation for Nordsieck methods

Abstract

Keywords

ASJC Scopus subject areas

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