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A differential geometric approach to singular perturbations

F. Jamitzky
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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.

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F. Jamitzky. 1997-08-04. A differential geometric approach to singular perturbations. https://arxiv.org/abs/physics/9708001

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