where B0 and β are suitably chosen to yield a
well-posed problem. We show that IDeC based on the
implicit Euler method performs satisfactorily while
for higher order methods like the box scheme or the trapezoidal
rule, order reductions occur. This is due to the break-down of
the asymptotic expansions of the global error caused by the singularity.
Also, a comparison with extrapolation methods is made.
Moreover, we explain why IDeC does not work in general
for terminal value problems of the form