On the Discrete Galerkin Method for Fredholm Integral Equations of the Second Kind

In the present paper, we refine some previous results on thediscrete Galerlcin method and the discrete iterated Galerkinmethod for Fredholm integral equations of the second kind. Byconsidering discrete inner products and discrete projectionson the same node points but with different quadrature rules,we are able to treat more appropriately kernels with discontinuousderivatives. In particular, for Green's function kernels weobtain a Nystr?m-type method which has the same order of convergenceas the corresponding Nystr?m method for infinitely smooth kernels.