RESUMEN

A previous work on the time discretization for the solution of a Volterra equation with completely monotonic convolution kernel is extended. The considered time discretization method comes from Part I [X. Da, IMA J. Numer. Anal., 22 (2002), pp. 133–151], where the backward Euler is combined with order one convolution quadrature approximating the integral. In the present paper, the convergence properties of the discretization in time are given in the $l_{t}^{1}(0,\infty;H)\bigcap l_{t}^{\infty}(0,\infty;H)$ norm.