Projection Methods

Abstract

The application of the quadrature method, in principle, is confined to equations of the second kind. In order to develop numerical methods which can also be used for equations of the first kind we now 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 which have been developed in the literature. Our presentation is meant as an introduction into these methods by studying their basic concepts and by describing their numerical performance through a few typical examples.