Superconvergent methods based on quasi-interpolating operators for fredholm integral equations of the second kind

In this paper, we apply spline quasi-interpolating operators on a bounded interval to solve numerically linear Fredholm integral equations of second kind by using superconvergent Nyström and degenerate kernel methods introduced in [4]. We give convergence orders associated with approximate solutions and their iterated versions in terms of spline quasi-interpolating order. Moreover, asymptotic expansions at the node/partition points for second kind Fredholm integral equations with Green's type kernel are obtained in the Nyström method based on quadratic and cubic quasi-interpolants. Therefore, the Richardson extrapolation technique is used to improve the convergence orders. Finally, numerical examples and comparison with existing methods are given to illustrate the theoretical results and to show that the proposed methods improve the convergence orders.