Abstract
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. 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.
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