A new approach to error estimation for general linear methods

J. C. Butcher; Zdzislaw Jackiewicz

doi:10.1007/s00211-002-0452-7

A new approach to error estimation for general linear methods

J. C. Butcher
, Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

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

28 Scopus citations

Abstract

We present a simple, accurate and reliable approach to the estimation of the local discretization error for general linear methods for ordinary differential equations. In this approach the input vector for the next step from x_n to x_n+1 = x_n + h is rescaled and modified accordingly to compensate for the change of stepsize from h̄ to h = r/h̄.

Original language	English (US)
Pages (from-to)	487-502
Number of pages	16
Journal	Numerische Mathematik
Volume	95
Issue number	3
DOIs	https://doi.org/10.1007/s00211-002-0452-7
State	Published - Sep 1 2003

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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title = "A new approach to error estimation for general linear methods",

abstract = "We present a simple, accurate and reliable approach to the estimation of the local discretization error for general linear methods for ordinary differential equations. In this approach the input vector for the next step from xn to xn+1 = xn + h is rescaled and modified accordingly to compensate for the change of stepsize from {\=h} to h = r/{\=h}.",

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AU - Jackiewicz, Zdzislaw

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N2 - We present a simple, accurate and reliable approach to the estimation of the local discretization error for general linear methods for ordinary differential equations. In this approach the input vector for the next step from xn to xn+1 = xn + h is rescaled and modified accordingly to compensate for the change of stepsize from h̄ to h = r/h̄.

AB - We present a simple, accurate and reliable approach to the estimation of the local discretization error for general linear methods for ordinary differential equations. In this approach the input vector for the next step from xn to xn+1 = xn + h is rescaled and modified accordingly to compensate for the change of stepsize from h̄ to h = r/h̄.

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UR - https://www.scopus.com/pages/publications/0345060035#tab=citedBy

U2 - 10.1007/s00211-002-0452-7

DO - 10.1007/s00211-002-0452-7

M3 - Article

AN - SCOPUS:0345060035

SN - 0029-599X

VL - 95

SP - 487

EP - 502

JO - Numerische Mathematik

JF - Numerische Mathematik

IS - 3

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A new approach to error estimation for general linear methods

Abstract

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