Metodi ad un passo fortemente stabili per equazioni integrali di Volterra di seconda specie di tipo stiff

In this paper we propose some implicit methods for stiff Volterra integral equations of second kind. The methods are constructed on the integro-differential equation obtained by differentiation of the Volterra equation. The numerical schemes are derived using a class of A-stable and L-stable methods for ordinary differential equations (proposed by Liniger and Willoughby in [3]) associated with the Gregory quadrature formula. Related to the test equation: {Mathematical expression} we give the definition of A-stability and ℒ-stability for the proposed numerical methods how natural extension of the A-stability and L-stability for the schemes for solving ordinary differential equations. We show how we have to choose the parameters of the methods in order to obtain A-stability and ℒ-stability schemes. Because of these properties the proposed schemes are particularly advantageous in the case of stiff Volterra integral equations.