Diagonally implicit general linear methods for ordinary differential equations

J. C. Butcher, Zdzislaw Jackiewicz

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


We investigate some classes of general linear methods with s internal and r external approximations, with stage order q and order p, adjacent to the class with s=r=q=p considered by Butcher. We demonstrate that interesting methods exist also if s+1=r=q, p=q or q+1, s=r+1=q, p=q or q+1, and s=r=q, p=q+1. Examples of such methods are constructed with stability function matching the A-acceptable generalized Padé approximations to the exponential function.

Original languageEnglish (US)
Pages (from-to)452-472
Number of pages21
Issue number3
StatePublished - Sep 1993


  • General linear method
  • Subject classifications: AMS(MOS), 65L05, 65L07
  • order conditions
  • stability analysis

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics


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