Iterated defect correction collocation methods in the numerical solution of Volterra integro-differential equations

Abstract

The application of iterated correction methods to Volterra integrodifferential equations (VDIEs) is considered. Polynomial collocation methods are used as the basic method. The approximations obtained are then interpolated and corrected iteratively by adding the defect to the approximations obtained by the basic method, extending corresponding work which applies to ordinary differential and integral equations. Preliminary results are given.