  The introduction of a lattice converts a singular boundary-layer problem in
the continuum into a regular perturbation problem. However, the continuum limit
of the discrete problem is extremely nontrivial and is not completely
understood. This paper examines two singular boundary-layer problems taken from
mathematical physics, the instanton problem and the Blasius equation, and in
each case examines two strategies, Pade resummation and variational
perturbation theory, to recover the solution to the continuum problem from the
solution to the associated discrete problem. Both resummation procedures
produce good and interesting results for the two cases, but the results still
deviate from the exact solutions. To understand the discrepancy a comprehensive
large-order behavior analysis of the strong-coupling lattice expansions for
each of the two problems is done.
