The Linear Barycentric Rational Quadrature Method for Volterra Integral Equations

We introduce two direct quadrature methods based on linear rational interpolation for solving general Volterra integral equations of the second kind. The first, deduced by a direct application of linear barycentric rational quadrature given in former work, is shown to converge at the same rate, but is costly on long integration intervals. The second, based on a composite version of the rational quadrature rule, looses one order of convergence, but is much cheaper. Both require only a sample of the involved functions at equispaced nodes and yield a stable, infinitely smooth solution of most classical examples with machine precision. Math Subject Classification: 65R20, 45G10