Nordsieck representation of DIMSIMs

J. C. Butcher; P. Chartier; Zdzislaw Jackiewicz

doi:10.1023/A:1019195215402

Nordsieck representation of DIMSIMs

J. C. Butcher
, P. Chartier
, Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

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

41 Scopus citations

Abstract

A new representation for diagonally implicit multistage integration methods (DIMSIMs) is derived in which the vector of external stages directly approximates the Nordsieck vector. The methods in this formulation are zero-stable for any choice of variable mesh. They are also easy to implement since changing step-size corresponds to a simple rescaling of the vector of external approximations. The paper contains an analysis of local truncation error and of error accumulation in a variable step-size situation.

Original language	English (US)
Pages (from-to)	209-230
Number of pages	22
Journal	Numerical Algorithms
Volume	16
Issue number	2
DOIs	https://doi.org/10.1023/A:1019195215402
State	Published - 1997

Keywords

DIMSIM methods
Error accumulation
Error estimation
Nordsieck representation
Variable step-size

ASJC Scopus subject areas

Applied Mathematics

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10.1023/A:1019195215402

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title = "Nordsieck representation of DIMSIMs",

abstract = "A new representation for diagonally implicit multistage integration methods (DIMSIMs) is derived in which the vector of external stages directly approximates the Nordsieck vector. The methods in this formulation are zero-stable for any choice of variable mesh. They are also easy to implement since changing step-size corresponds to a simple rescaling of the vector of external approximations. The paper contains an analysis of local truncation error and of error accumulation in a variable step-size situation.",

keywords = "DIMSIM methods, Error accumulation, Error estimation, Nordsieck representation, Variable step-size",

author = "Butcher, \{J. C.\} and P. Chartier 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 Foundation under grant NSF DMS-9208048. 1 The tensor product ∆ ⊗ Λ of two matrices ∆ 2 Rm1,m2",

year = "1997",

doi = "10.1023/A:1019195215402",

language = "English (US)",

volume = "16",

pages = "209--230",

journal = "Numerical Algorithms",

issn = "1017-1398",

publisher = "Springer Netherlands",

number = "2",

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TY - JOUR

T1 - Nordsieck representation of DIMSIMs

AU - Butcher, J. C.

AU - Chartier, P.

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 Foundation under grant NSF DMS-9208048. 1 The tensor product ∆ ⊗ Λ of two matrices ∆ 2 Rm1,m2

PY - 1997

Y1 - 1997

N2 - A new representation for diagonally implicit multistage integration methods (DIMSIMs) is derived in which the vector of external stages directly approximates the Nordsieck vector. The methods in this formulation are zero-stable for any choice of variable mesh. They are also easy to implement since changing step-size corresponds to a simple rescaling of the vector of external approximations. The paper contains an analysis of local truncation error and of error accumulation in a variable step-size situation.

AB - A new representation for diagonally implicit multistage integration methods (DIMSIMs) is derived in which the vector of external stages directly approximates the Nordsieck vector. The methods in this formulation are zero-stable for any choice of variable mesh. They are also easy to implement since changing step-size corresponds to a simple rescaling of the vector of external approximations. The paper contains an analysis of local truncation error and of error accumulation in a variable step-size situation.

KW - DIMSIM methods

KW - Error accumulation

KW - Error estimation

KW - Nordsieck representation

KW - Variable step-size

UR - https://www.scopus.com/pages/publications/0141467986

UR - https://www.scopus.com/pages/publications/0141467986#tab=citedBy

U2 - 10.1023/A:1019195215402

DO - 10.1023/A:1019195215402

M3 - Article

SN - 1017-1398

VL - 16

SP - 209

EP - 230

JO - Numerical Algorithms

JF - Numerical Algorithms

IS - 2

ER -

Nordsieck representation of DIMSIMs

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Keywords

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