Regularity properties of multistage integration methods

Zdzislaw Jackiewicz, R. Vermiglio, M. Zennaro

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The numerical method for ordinary differential equations is regular if it has the same set of finite asymptotic values as the underlying differential system. This paper examines the regularity and strong regularity properties of diagonally implicit multistage integration methods (DIMSIMs) introduced recently by J.C. Butcher. A sufficient condition for regularity and strong regularity of such methods of any order is given and it is proved that this condition is also necessary for two-step two-stage DIMSIMs of order greater than or equal to two. It is also demonstrated that there exist regular schemes in the class of explicit DIMSIMs. This is in contrast to explicit Runge-Kutta methods with more than one stage, which are always irregular.

Original languageEnglish (US)
Pages (from-to)285-302
Number of pages18
JournalJournal of Computational and Applied Mathematics
Volume87
Issue number2
StatePublished - Dec 23 1997

Fingerprint

Regularity Properties
Strong Regularity
Runge Kutta methods
Regularity
Ordinary differential equations
Numerical methods
Explicit Methods
Runge-Kutta Methods
Differential System
Irregular
Ordinary differential equation
Numerical Methods
Necessary
Sufficient Conditions

Keywords

  • Asymptotic values
  • General linear method
  • Ordinary differential equation
  • Regularity

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Regularity properties of multistage integration methods. / Jackiewicz, Zdzislaw; Vermiglio, R.; Zennaro, M.

In: Journal of Computational and Applied Mathematics, Vol. 87, No. 2, 23.12.1997, p. 285-302.

Research output: Contribution to journalArticle

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