The acceleration technique known as Iterated Defect Correction
(IDeC) for the numerical solution of singular initial value problems
is investigated. IDeC based on the implicit Euler method performs
satisfactorily and can thus be used for the efficient solution
of singular boundary value problems with the shooting method.
Higher order one-step methods like the box scheme or the
trapezoidal rule cannot serve as a basic method because of a break-down
of the asymptotic expansions of the global error caused by the
singularity. The theoretical considerations are also supported
by a comparison with extrapolation methods. Finally, it is shown that
for similar reasons IDeC cannot be used for singular
terminal value problems.