Nystrom methods for Fredholm integral equations using equispaced points

In this paper we investigate some Nystr¨om methods for Fredholm integral equations in the interval [0, 1]. We give an overview of the order of convergence, which depends on the smoothness of the involved functions. In particular, we consider the Nystr¨om methods based on the so called Generalized Bernstein quadrature rule, on a Romberg scheme and on the so-called IMT rule. We prove that the proposed methods are convergent, stable and well conditioned. Also, we give several numerical tests for comparing these three methods