  We introduce an alternative to the method of matched asymptotic expansions.
In the "traditional" implementation, approximate solutions, valid in different
(but overlapping) regions are matched by using "intermediate" variables. Here
we propose to match at the level of the equations involved, via a "uniform
expansion" whose equations enfold those of the approximations to be matched.
This has the advantage that one does not need to explicitly solve the
asymptotic equations to do the matching, which can be quite impossible for some
problems. In addition, it allows matching to proceed in certain wave situations
where the traditional approach fails because the time behaviors differ (e.g.,
one of the expansions does not include dissipation). On the other hand, this
approach does not provide the fairly explicit approximations resulting from
standard matching. In fact, this is not even its aim, which to produce the
"simplest" set of equations that capture the behavior.

Fluid Dynamics