Discrete superconvergent Nyström method for integral equations and eigenvalue problems

In this paper, discrete superconvergent Nyström method is studied for solving the second kind Fredholm integral equations and eigenvalue problems of a compact integral operator with a smooth kernel. We use interpolatory projections at Gauss points onto the space of (discontinuous) piecewise polynomials of degree ≤r−1≤r−1. We analyze the convergence of this method and its iterated version and we establish superconvergence results. Numerical examples are presented to illustrate the obtained theoretical estimates.