On spline approximation for a class of integral equations. I: Galerkin and collocation methods with piecewise polynomials

We consider the numerical solution of a class of one-dimensional non-compact integral equations by Galerkin and collocation methods and their iterated variants, using piecewise polynomials as basis functions. In particular, we obtain new results for the stability of the approximation methods, without any restriction on the norm of the integral operators. Furthermore, we extend results of Chandler and Graham^4,6 concerning error estimates and superconvergence to a more general class of operators.