Quasi Interpolation Methods for Linear Volterra Integral Equations

In this paper, we present a numerical method for solving linear Volterra integral equations of the second kind based on approximating the solution by spline quasi-interpolant operators. Such a method is stable in the whole interval, preserves the smoothness of the exact solution and gives convergence in the uniform norm. Global convergence errors are given for approximate solution, its derivatives and the iterated solution. Moreover, a local superconvergence at some particular points is shown for the approximate solution. We also analyzed the discrete version of the method obtained by suitable numerical quadrature. Finally, numerical tests supporting theoretical results and comparison with several methods on the existing literature are given.