On the solution of Fredholm integral equations based on spline quasi-interpolating projectors

Abstract

We use spline quasi-interpolating projectors on a bounded interval for the numerical solution of linear Fredholm integral equations of the second kind by Galerkin, Kantorovich, Sloan and Kulkarni schemes. We get theoretical results related to the convergence order of the methods, in case of quadratic and cubic spline projectors, and we describe computational aspects for the construction of the approximate solutions. Finally, we give several numerical examples, that confirm the theoretical results and show that higher orders of convergence can be obtained by Kulkarni’s scheme.