High-order quadrature rules based on spline quasi-interpolants and application to integral equations

In this paper, we present a class of quadrature rules with endpoint corrections based on integrating spline quasi-interpolants. The correction weights are obtained as solutions of certain systems of linear algebraic equations. We give a comparison between the rules obtained here and the Gregory rules of the same order. Furthermore, an application of these quadrature rules to the numerical solution of Fredholm integral equations of the second kind is worked out in detail. Numerical examples illustrating the theory are given.