Spectral Approximation Methods for Fredholm Integral Equations with Non-Smooth Kernels

In this paper, polynomially based projection and modified projection methods for approximating the solution of Fredholm integral equations with a kernel of Green's function type are studied. The projection is either an orthogonal projec- tion or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and those of superconvergence of the iterated versions are analysed. A numerical example is given to illustrate the theoretical results.