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.
Construction of highly stable Volterra Runge-Kutta methods / D., Conte; R., D'Ambrosio; Izzo, Giuseppe; Z., Jackiewicz. - (2013). (Intervento presentato al convegno ANODE 2013 - Auckland Numerical Ordinary Differential Equations tenutosi a Auckland (New Zealand) nel 7-11/01/2013).
Construction of highly stable Volterra Runge-Kutta methods
IZZO, GIUSEPPE;
2013
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
