Implementation of diagonally implicit multistage integration methods for ordinary differential equations

J. C. Butcher, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

59 Scopus citations

Abstract

We investigate the implementation of diagonally implicit multistage integration methods (DIMSIMs). The implementation issues addressed are the local error estimation, changing stepsize using the Nordsieck technique, and the construction of continuous interpolants. Numerical experiments with a method of order three indicate that the error estimates that have been constructed are very reliable in both a fixed and a variable stepsize environment.

Original languageEnglish (US)
Pages (from-to)2119-2141
Number of pages23
JournalSIAM Journal on Numerical Analysis
Volume34
Issue number6
DOIs
StatePublished - Jan 1 1997

Keywords

  • Continuous interpolants
  • General linear method
  • Local error estimation
  • Nordsieck technique

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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