Year: 1997
Type: preprint
Abstract: A differential geometric approach to singular perturbation theory is presented. It is shown that singular perturbation problems such as multiple-scale and boundary layer problems can be treated more easily on a differential geometric basis. A general method is proposed based on differential forms and Lie-derivatives. Examples from multiple scale theory, boundary layer theory and WKB-theory are given and it is demonstrated that without the a priori knowledge of the scaling behaviour of the problem the correct asymptotic expansion can be derived with the aid of differential forms. The method is well suited for a mechanical implementation in computer algebra programs.
Source: arXiv (Cornell University)
Author: Jamitzky, F.
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1643866293