Sull’analisi numerica delle equazioni integrali di Volterra

Abstract

In this note we examine a fourth-order Runge-Kutta procedure for the nn-meric resolution of Volterra integral equation: $$y(t) = f(t) - \int\limits_{t_0 }^t {\varphi (t, \tau , y (\tau )) } d\tau$$ . This procedure is a generalitation of the one proposed by E. Aparo in [1] and improved by M. H. Onles in [2], [3], [4] and permits to calculate the approximate values ofy(t 0 +ih) fori=1, 2, ...,n. This note contains the theoretical demonstration of the convergence of the proposed approximation procedure.