Nordsieck methods with computationally verified algebraic stability

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Abstract

We describe the search for algebraically stable Nordsieck methods of order p = s and stage order q = p, where s is the number of stages. This search is based on the theoretical criteria for algebraic stability proposed recently by Hill, and Hewitt and Hill, for general linear methods for ordinary differential equations. These criteria, which are expressed in terms of the non-negativity of the eigenvalues of a Hermitian matrix on the unit circle, are then verified computationally for the derived Nordsieck methods of order p ≥ 2.

Original languageEnglish (US)
Pages (from-to)8598-8610
Number of pages13
JournalApplied Mathematics and Computation
Volume217
Issue number21
DOIs
StatePublished - Jul 1 2011

Keywords

  • Algebraic stability
  • General linear methods
  • Nordsieck methods
  • Order conditions

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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