Projection Methods

Abstract

The application of the quadrature method, in principle, is confined to equations of the second kind. To develop numerical methods that can also be used for equations of the first kind we will describe projection methods as a general tool for approximately solving operator equations. After introducing into the principal ideas of projection methods and their convergence and error analysis we shall consider collocation and Galerkin methods as special cases. We do not intend to give a complete account of the numerous implementations of collocation and Galerkin methods for integral equations that have been developed in the literature. Our presentation is meant as an introduction to these methods by studying their basic concepts and describing their numerical performance through a few typical examples.