Construction of general linear methods with Runge-Kutta stability properties

J. C. Butcher, Zdzislaw Jackiewicz

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

We describe the construction of explicit general linear methods of order p and stage order q = p with s = p + 1 stages which achieve good balance between accuracy and stability properties. The conditions are imposed on the coefficients of these methods which ensure that the resulting stability matrix has only one nonzero eigenvalue. This eigenvalue depends on one real parameter which is related to the error constant of the method. Examples of methods are derived which illustrate the application of the approach presented in this paper.

Original languageEnglish (US)
Pages (from-to)53-72
Number of pages20
JournalNumerical Algorithms
Volume36
Issue number1
DOIs
StatePublished - May 1 2004

Keywords

  • General linear methods
  • Inherent Runge-Kutta stability
  • Nordsieck representation

ASJC Scopus subject areas

  • Applied Mathematics

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