Quadrature Methods

Abstract

In this chapter we shall describe the quadratureor Nyström methodfor the approximate solution of integral equations of the second kind with continuous or weakly singular kernels. As we have pointed out in Chapter 11, the implementation of the degenerate kernel method, in general, requires some use of numerical quadrature. Therefore it is natural to try the application of numerical integration in a more direct approach to approximate integral operators by numerical integration operators. This will lead to a straightforward but widely applicable method for approximately solving equations of the second kind. The reason we placed the description of the quadrature method after the degenerate kernel method is only because its error analysis is more involved.