A reliable error estimation for diagonally implicit multistage integration methods

J. C. Butcher; Zdzislaw Jackiewicz

doi:10.1023/A:1021987717046

A reliable error estimation for diagonally implicit multistage integration methods

J. C. Butcher, Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

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

22 Scopus citations

Abstract

A new approach to the estimation of the local discretization error for diagonally implicit multistage integration methods (DIMSIMs) is described. The error estimates that are obtained are very accurate and very reliable for both explicit and implicit methods for any stepsize pattern.

Original language	English (US)
Pages (from-to)	656-665
Number of pages	10
Journal	BIT Numerical Mathematics
Volume	41
Issue number	4
DOIs	https://doi.org/10.1023/A:1021987717046
State	Published - Dec 2001

Keywords

DIMSIM methods
Local error estimation
Nordsieck representation

ASJC Scopus subject areas

Software
Computer Networks and Communications
Computational Mathematics
Applied Mathematics

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10.1023/A:1021987717046

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title = "A reliable error estimation for diagonally implicit multistage integration methods",

abstract = "A new approach to the estimation of the local discretization error for diagonally implicit multistage integration methods (DIMSIMs) is described. The error estimates that are obtained are very accurate and very reliable for both explicit and implicit methods for any stepsize pattern.",

keywords = "DIMSIM methods, Local error estimation, Nordsieck representation",

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

note = "Funding Information: ∗Received May 2000. Communicated by Syvert P. N{\o}rsett. †The work of the first author was assisted by the Marsden Fund of New Zealand. The work of the second author was partially supported by the National Science Foundation under grant NSF DMS–9971164. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",

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AU - Butcher, J. C.

AU - Jackiewicz, Zdzislaw

N1 - Funding Information: ∗Received May 2000. Communicated by Syvert P. Nørsett. †The work of the first author was assisted by the Marsden Fund of New Zealand. The work of the second author was partially supported by the National Science Foundation under grant NSF DMS–9971164. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2001/12

Y1 - 2001/12

N2 - A new approach to the estimation of the local discretization error for diagonally implicit multistage integration methods (DIMSIMs) is described. The error estimates that are obtained are very accurate and very reliable for both explicit and implicit methods for any stepsize pattern.

AB - A new approach to the estimation of the local discretization error for diagonally implicit multistage integration methods (DIMSIMs) is described. The error estimates that are obtained are very accurate and very reliable for both explicit and implicit methods for any stepsize pattern.

KW - DIMSIM methods

KW - Local error estimation

KW - Nordsieck representation

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A reliable error estimation for diagonally implicit multistage integration methods

Abstract

Keywords

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