We investigate collocation methods for the efficient solution of
singular boundary value problems with an essential singularity. We
give numerical evidence that this approach indeed yields high
order solutions. Moreover, we discuss the issue of a posteriori
error estimation for the collocation solution. An estimate based
on the defect correction principle, which has been successfully
applied to problems with a singularity of the first kind, is less
robust with respect to an essential singularity than a classical
strategy based on mesh halving.