Nordsieck representation of DIMSIMs

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

Research output: Contribution to journalArticle

35 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)209-230
Number of pages22
JournalNumerical Algorithms
Volume16
Issue number2
StatePublished - 1997

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Variable Step Size
Truncation Error
Rescaling
Mesh
Formulation
Zero
Approximation

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Butcher, J. C., Chartier, P., & Jackiewicz, Z. (1997). Nordsieck representation of DIMSIMs. Numerical Algorithms, 16(2), 209-230.

Nordsieck representation of DIMSIMs. / Butcher, J. C.; Chartier, P.; Jackiewicz, Zdzislaw.

In: Numerical Algorithms, Vol. 16, No. 2, 1997, p. 209-230.

Research output: Contribution to journalArticle

Butcher, JC, Chartier, P & Jackiewicz, Z 1997, 'Nordsieck representation of DIMSIMs', Numerical Algorithms, vol. 16, no. 2, pp. 209-230.
Butcher JC, Chartier P, Jackiewicz Z. Nordsieck representation of DIMSIMs. Numerical Algorithms. 1997;16(2):209-230.
Butcher, J. C. ; Chartier, P. ; Jackiewicz, Zdzislaw. / Nordsieck representation of DIMSIMs. In: Numerical Algorithms. 1997 ; Vol. 16, No. 2. pp. 209-230.
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