Ef-Gaussian direct quadrature methods for Volterra integral equations with periodic solution

A direct quadrature method for the solution of Volterra integral equations with periodic solution is proposed. This method is based on an exponentially fitted quadrature rule of Gaussian type, whose parameters depend on the problem, in order to reproduce the behavior of the analytical solution. The error of the quadrature rule is examined and a convergence analysis of the direct quadrature method is given. Some numerical experiments are presented for comparison with other existing methods.