grad student project? singularly perturbed differential equations
Subject: grad student project? singularly perturbed differential equations
From: Evgeniy Maevskiy
Date: Thu, 07 Jun 2012 21:59:23 +0300
We already have a package for regularly perturbed differential
equations? There, too, is not simple, but it is much easier than in the
singular case.
07.06.2012 17:58, Richard Fateman ?????:
> 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?