Discrete Collocation Methods for Second Kind Fredholm Integral Equations

Abstract

The numerical solution of second kind Fredholm integral equations by the discrete collocation method and a discrete iterated collocation method is studied. Orders of convergence for the two discrete methods are given for the case in which an interpolatory quadrature rule of appropriate precision is used. If the kernel is sufficiently smooth, these orders of convergence will be the same as those of the exact methods. Some numerical results are given.