grad student project? singularly perturbed differential equations



This topic appears repeatedly as a possible application of computer algebra
systems, starting from at least W.A. Martin's MIT dissertation (c. 1966).

In SIAM Review vol 54, no. 2 pp 374-388 there is a tutorial paper
"The Renormalization Group: A Perturbation Method for the Graduate 
Curriculum"
by E. Kirkinis

which includes the sentence "Since the RG method is clear and 
systematic, there
is room to develop commercial symbolic computation software packages."

The [ancient?] history of solving perturbed D.E.s consists of examining 
a few
particular equations and coming up with "methods" that work on them but 
maybe not
on others.  I say "methods" because the texts describe them as
  typically isolated examples.

There is a large literature but I think that newer texts
tend to include whatever worked in the prior literature.

This RG may in fact be more of a unifying approach (looks sort of like the
method of multiple scales).

Any applied math grad students out there?