The iterated projection solution for the Fredholm integral equation of second kind

Abstract

AbstractWe are concerned with the solution of the second kind Fredholm equation (and eigenvalue problem) by a projection method, where the projection is either an orthogonal projection on a set of piecewise polynomials or an interpolatory projection at the Gauss points of subintervals.We study these cases of superconvergence of the Sloan iterated solution: global superconvergence for a smooth kernel, and superconvergence at the partition points for a kernel of “Green's function” type. The mathematical analysis applies for the solution of the inhomogeneous equation as well as for an eigenvector.