Error Estimates of Projection Type Methods for Solving Weakly Singular Integral Equations

Abstract

We study projection type methods for numerical solution of one class of weakly singular integral Fredholm equations of the second kind including the integral radiative transfer equation. We consider Galerkin type methods and their modifications: the iterated Galerkin method (the Sloan method), the Kantorovich method, and the iterated Kantorovich method. For the approximating space we take the space of piecewise constant functions or the space of piecewise linear functions related to an arbitrary nonuniform grid. Error estimates are obtained.