BIT Numerical Mathematics

, Volume 27, Issue 3, pp 403–423 | Cite as

Relationships among some classes of implicit Runge-Kutta methods and their stability functions

  • P. H. Muir
  • W. H. Enright
Part II Numerical Mathematics

Abstract

In this paper we apply the theory for implicit Runge-Kutta methods presented by Stetter to a number of subclasses of methods that have recently been discussed in the literature. We first show how each of these classes can be expressed within this theoretical framework and from this we are able to establish a number of relationships among these classes. In addition to improving the current state of understanding of these methods, their expression within this theoretical framework makes it possible for us to obtain results giving general forms for their stability functions.

AMS categories

65L05 65L20 34A50 

Keywords

Runge-Kutta methods reflected methods symmetric methods efficiency 

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Copyright information

© BIT Foundations 1987

Authors and Affiliations

  • P. H. Muir
    • 1
    • 2
  • W. H. Enright
    • 1
    • 2
  1. 1.Department of Mathematics and Computing ScienceSaint Mary's UniversityHalifaxCanada
  2. 2.Department of Computer ScienceUniversity of TorontoTorontoCanada

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