Generalized linear multistep methods for ordinary differential equations

Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper we use the theoretical framework of General Linear Methods (GLMs) to analyze and generalize the class of Cash's Modified Extended Backward Differentiation Formulae (MEBDF). Keeping the structure of MEBDF and their computational cost we propose a more general class of methods that can be viewed as a composition of modified linear multistep methods. These new methods are characterized by smaller error constants and possibly larger angles of A(α)-stability. Numerical experiments which confirm the good performance of these methods on a set of stiff problems are also reported.

Original languageEnglish (US)
Pages (from-to)165-178
Number of pages14
JournalApplied Numerical Mathematics
Volume114
DOIs
StatePublished - Apr 1 2017

Keywords

  • A(α)-stability
  • A-stability
  • Error constants
  • Extended Backward Differentiation Formulae
  • L(α)-stability
  • L-stability
  • MEBDF
  • PMEBDF
  • Stiff problems

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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