Search for highly stable two-step Runge-Kutta methods

R. D'Ambrosio, G. Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

We describe the search for A-stable and algebraically stable two-step Runge Kutta methods of order p and stage order q=p or q=p-1. The search for A-stable methods is based on the Schur criterion applied for specific methods with stability polynomial of reduced degree. The search for algebraically stable methods is based on the criteria proposed recently by Hewitt and Hill.

Original languageEnglish (US)
Pages (from-to)1361-1379
Number of pages19
JournalApplied Numerical Mathematics
Volume62
Issue number10
DOIs
StatePublished - Oct 2012

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Two-step Runge-Kutta Methods
Runge Kutta methods
Polynomials
Polynomial

Keywords

  • A-stability
  • Algebraic stability
  • Linear stability analysis
  • Order conditions
  • Two-step Runge-Kutta methods

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Search for highly stable two-step Runge-Kutta methods. / D'Ambrosio, R.; Izzo, G.; Jackiewicz, Zdzislaw.

In: Applied Numerical Mathematics, Vol. 62, No. 10, 10.2012, p. 1361-1379.

Research output: Contribution to journalArticle

D'Ambrosio, R. ; Izzo, G. ; Jackiewicz, Zdzislaw. / Search for highly stable two-step Runge-Kutta methods. In: Applied Numerical Mathematics. 2012 ; Vol. 62, No. 10. pp. 1361-1379.
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