Natural Volterra Runge-Kutta methods

Authors:
Dajana Conte;Raffaele D'ambrosio;Giuseppe Izzo;Zdzislaw Jackiewicz
Affiliations:
University of Salerno, Fisciano, Italy;University of Salerno, Fisciano, Italy;University of Naples "Federico II", Naples, Italy;Arizona State University, Tempe, USA and AGH University of Science and Technology, Kraków, Poland
Venue:
Numerical Algorithms
Year:
2014

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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 V0-stable methods is described and examples of highly stable methods are presented up to the order p = 4 and stage order q = 4.