Implementation of diagonally implicit multistage integration methods for ordinary differential equations

J. C. Butcher, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

56 Citations (Scopus)

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
StatePublished - 1997

Fingerprint

Ordinary differential equations
Error analysis
Ordinary differential equation
Local Error Estimation
Variable Step Size
Interpolants
Error Estimates
Experiments
Numerical Experiment

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Implementation of diagonally implicit multistage integration methods for ordinary differential equations. / Butcher, J. C.; Jackiewicz, Zdzislaw.

In: SIAM Journal on Numerical Analysis, Vol. 34, No. 6, 1997, p. 2119-2141.

Research output: Contribution to journalArticle

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