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 lₜ¹(0,∞;H) lₜ∞(0,∞;H) norm.
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Da Xu (2008) studied this question.
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