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Numerical Algorithms

, Volume 65, Issue 3, pp 421–445 | Cite as

Natural Volterra Runge-Kutta methods

  • Dajana Conte
  • Raffaele D’Ambrosio
  • Giuseppe Izzo
  • Zdzislaw Jackiewicz
Original Paper

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.

Keywords

Volterra integral equation Volterra Runge-Kutta methods Order and stage order conditions Stability analysis A-stability V0-stability 

Mathematics Subject Classification (2010)

65R20 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Dajana Conte
    • 1
  • Raffaele D’Ambrosio
    • 1
  • Giuseppe Izzo
    • 2
  • Zdzislaw Jackiewicz
    • 3
    • 4
  1. 1.University of SalernoFiscianoItaly
  2. 2.University of Naples “Federico II”NaplesItaly
  3. 3.Arizona State UniversityTempeUSA
  4. 4.AGH University of Science and TechnologyKrakówPoland

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