Algebraically stable diagonally implicit general linear methods

Laura L Hewitt, Adrian T Hill

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

This paper concerns algebraically stable diagonally implicit general linear methods, intended for stiff differential equations. The first step in the construction of such methods is to apply the order theory from the series of papers by Butcher and Jackiewicz. The order theory and structural assumptions leave a number of free parameters, which may be chosen to make the method both simple and algebraically stable. Here, this choice is made by applying new sufficient conditions for algebraic stability. Methods of 2 steps and 2 stages are constructed with stage order 2, and total order up to 4.
Original languageEnglish
Pages (from-to)629-636
Number of pages8
JournalApplied Numerical Mathematics
Volume60
Issue number6
DOIs
Publication statusPublished - Jun 2010

Keywords

  • algebraic stability
  • DIMSIMs
  • stiff problems
  • general linear methods

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