Volterra discrete equations: Summability of the fundamental matrix (Q5952133)

In order to obtain insight into the stability analysis of numerical methods (direct quadrature methods of order up to three) for linear Volterra integral equations of the second-kind, the author derives sufficient conditions for the summability of the ``discrete resolvent kernel'' associated with the Volterra difference equation \[ x_n =\sum^n_{\ell=n_0} a_{n,\ell} x_\ell+g_n,\quad n\geq n_0. \] They are based on sign and monotonicity properties of the given discrete kernel \(\{a_{n,\ell}\}\).