On the order of the error in discretization methods for weakly singular second kind non-smooth solutions

In general, second kind Volterra integral equations with weakly singular kernels of the formk(t,s)(t −s)−α posses solutions which have discontinuous derivatives att=0. A discrete Gronwall inequality is employed to prove that, away from the origin, the error in product integration and collocation schemes for these equations is of order 2-α.