We discuss a new variant of Iterated Defect Correction
(IDeC), which increases the range of applicability of the
method.
Splitting methods are utilized in conjunction with
special integration methods for Hamiltonian systems, or other
initial value problems for ordinary differential equations with a
particular structure, to solve the neighboring problems
occurring in the course of the IDeC iteration. We demonstrate that
this acceleration technique serves to rapidly increase the
convergence order of the resulting numerical approximations, up to
the theoretical limit given by the order of certain
superconvergent collocation methods.