On mixed collocation methods for Volterra integral equations with periodic solution

Abstract

In this paper we extend recent results for the numerical solution of Volterra integro-differential equations with periodic solution (Brunner, Makroglou and Miller, 1996) to the numerical solution of Volterra integral equations with periodic solution. We apply collocation and iterated collocation methods based on the mixed interpolation methods of De Meyer, Vanthournout and Vanden Berghe (1990). The existence of unique continuous periodic solutions is examined and a convergence analysis of the numerical method is given. Numerical results are included for comparison with the polynomial collocation methods based on Lobatto and Gauss points as collocation parameters.