dorsal/arxiv
View SchemaA differential geometric approach to singular perturbations
| Authors | F. Jamitzky |
|---|---|
| Categories | |
| ArXiv ID | physics/9708001 |
| URL | https://arxiv.org/abs/physics/9708001 |
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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"abstract": "A differential geometric approach to singular perturbation theory is\npresented. It is shown that singular perturbation problems such as\nmultiple-scale and boundary layer problems can be treated more easily on a\ndifferential geometric basis. A general method is proposed based on\ndifferential forms and Lie-derivatives. Examples from multiple scale theory,\nboundary layer theory and WKB-theory are given and it is demonstrated that\nwithout the a priori knowledge of the scaling behaviour of the problem the\ncorrect asymptotic expansion can be derived with the aid of differential forms.\nThe method is well suited for a mechanical implementation in computer algebra\nprograms.",
"arxiv_id": "physics/9708001",
"authors": [
"F. Jamitzky"
],
"categories": [
"math-ph",
"math.MP"
],
"title": "A differential geometric approach to singular perturbations",
"url": "https://arxiv.org/abs/physics/9708001"
},
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