General linear methods with external stages of different orders

Zdzislaw Jackiewicz, R. Vermiglio

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


The approach introduced recently by Albrecht to derive order conditions for Runge-Kutta formulas based on the theory of A-methods is also very powerful for the general linear methods. In this paper, using Albrecht's approach, we formulate the general theory of order conditions for a class of general linear methods where the components of the propagating vector of approximations to the solution have different orders. Using this theory we derive a class of diagonally implicit multistage integration methods (DIMSIMs) for which the global order is equal to the local order. We also derive a class of general linear methods with two nodal approximations of different orders which facilitate local error estimation. Our theory also applies to the class of two-step Runge-Kutta introduced recently by Jackiewicz and Tracogna.

Original languageEnglish (US)
Pages (from-to)688-712
Number of pages25
JournalBIT Numerical Mathematics
Issue number4
StatePublished - Dec 1996


  • Error estimation
  • General linear methods
  • Order conditions
  • Stage errors

ASJC Scopus subject areas

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


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