Spline quasi-interpolating projectors for the solution of nonlinear integral equations

In this paper we use spline quasi-interpolating projectors on a bounded interval for the numerical solution of nonlinear integral equations. In particular, we propose a spline quasi-interpolating projection method with high order of convergence and a spline quasiinterpolating collocation method, both in case of smooth kernels and in case of Green’s function type ones. We explicitly construct the approximate solutions and we get results related to the convergence orders. Finally, we provide numerical tests, that confirm the theoretical results.