Search for efficient general linear methods for ordinary differential equations

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We analyze implicit general linear methods with s internal stages and r=s+1 external stages of order p=s+1 and stage order q=s or q=s+1. These methods might eventually lead to more efficient formulas than the class of DIMSIMs and the class of general linear methods with inherent Runge-Kutta stability. We analyze also error propagation and estimation of local discretization errors. Examples of such methods which are A- and L-stable are derived up to the stage order q=3 or q=4 and order p=4.

Original languageEnglish (US)
Pages (from-to)180-192
Number of pages13
JournalJournal of Computational and Applied Mathematics
Volume262
DOIs
StatePublished - May 15 2014

Keywords

  • A- and L-stability
  • Construction of highly stable methods
  • Error propagation
  • General linear methods
  • Order and stage order
  • Order conditions

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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