On the boundary layer methods (Q1087711)

The defect of the traditionary boundary layer methods (including the method of matched asymptotic expansions and the method of Visik- Lyusternik) is noted, from those methods we can not construct the asymptotic expansion of boundary layer term substantially. So the method of multiple scales is proposed for constructing the asymptotic expansion of boundary layer term, the reasonable result is obtained. Furthermore, we compare this method with the method used by Levinson, and find that both methods give the same asymptotic expansion of boundary layer term, but our method is simpler. Again, we apply this method to study some known works on singular perturbations. The limitations of those works have been noted, and the asymptotic expansion of solution is constructed in general condition.