Higher Accuracy Methods for Second-Kind Volterra Integral Equations Based on Asymptotic Expansions of Iterated Galerkin Methods

Abstract

On the basis of asymptotic expansions, we study the Richardson extrapolation method and two defect correction schemes by an interpolation post-processing technique, namely, interpolation correction and iterative correction for the numerical solution of a Volterra integral equation by iterated finite element methods. These schemes are of higher accuracy than the postprocessing method and analyzed in a recent paper [5] by Brunner, Q. Lin and N. Yan. Moreover, we give a positive answer to a conjecture in [5].