Iterated defect correction for the solution of singular initial value problems

We investigate the convergence properties of the iterated defect correction (IDeC) method based on the implicit Euler rule for the solution of singula r initial value problems with a singularity of the first kind. We show that the method retains its classical order of convergence, which means that th e sequence of approximations obtained during the iteration shows gradually growing order of convergence limited by the smoothness of the data and tech nical details of the procedure.