Nordsieck representation of DIMSIMs

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

Research output: Contribution to journalArticle

35 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 languageEnglish (US)
Pages (from-to)209-230
Number of pages22
JournalNumerical Algorithms
Volume16
Issue number2
DOIs
StatePublished - Jan 1 1997

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

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