On asymptotic error expansions for singular boundary value problems

The existence of an asymptotic expansion for the global error of a standard three-point finite difference scheme applied to solve BVPs for ordinary di fferential equations of second order with a singularity of the first kind i s considered. It turns out that even for very smooth problem data such asym ptotic expansion does not exist, in general. More precisely, its length is restricted by unbounded inhomogeneities occurring in Variational equations due to the singularity.