Iteration methods for Fredholm integral equations of the second kind based on spline quasi-interpolants

In this paper, we propose an efficient iteration algorithm for Fredholm integral equations of the second kind based on spline quasi-interpolants (abbr. QIs). We show that for every iteration step we obtain superconvergence rates. A superconvergent method called functional approximation method based on QIs is also developed. We illustrate our results by numerical experiments.