Two postprocessing techniques for barycentric rational collocation methods applied to weakly singular VIEs

This paper investigates two postprocessing techniques for barycentric rational collocation methods for Volterra integral equations with weakly singular kernels. The interpolation postprocessing and iteration postprocessing techniques are respectively applied to the collocation solution of the transformed equations. It is proved that both postprocessing approximations possess higher order of global convergence, that is, global superconvergence. Numerical examples are also presented to verify the superconvergence results.