Natural Volterra Runge-Kutta methods

Dajana Conte, Raffaele D'Ambrosio, Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

A very general class of Runge-Kutta methods for Volterra integral equations of the second kind is analyzed. Order and stage order conditions are derived for methods of order p and stage order q = p up to the order four. We also investigate stability properties of these methods with respect to the basic and the convolution test equations. The systematic search for A- and V 0-stable methods is described and examples of highly stable methods are presented up to the order p = 4 and stage order q = 4.

Original languageEnglish (US)
Pages (from-to)421-445
Number of pages25
JournalNumerical Algorithms
Volume65
Issue number3
DOIs
StatePublished - Mar 1 2014

Keywords

  • A-stability
  • Order and stage order conditions
  • Stability analysis
  • V-stability
  • Volterra Runge-Kutta methods
  • Volterra integral equation

ASJC Scopus subject areas

  • Applied Mathematics

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