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The introduction of a lattice converts a singular boundary-layer problem inthe continuum into a regular perturbation problem. However, the continuum limitof the discrete problem is extremely nontrivial and is not completelyunderstood. This paper examines two singular boundary-layer problems taken frommathematical physics, the instanton problem and the Blasius equation, and ineach case examines two strategies, Pade resummation and variationalperturbation theory, to recover the solution to the continuum problem from thesolution to the associated discrete problem. Both resummation proceduresproduce good and interesting results for the two cases, but the results stilldeviate from the exact solutions. To understand the discrepancy a comprehensivelarge-order behavior analysis of the strong-coupling lattice expansions foreach of the two problems is done.Comment: 22 pages, 2 figures, submitted for publication in JM

Boundary-layer theory, strong-coupling series, and large-order behavior