Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Necessary conditions for applicability of Poincaré-Lighthill perturbation theory


Author: Peter D. Usher
Journal: Quart. Appl. Math. 28 (1971), 463-471
MSC: Primary 34.53
DOI: https://doi.org/10.1090/qam/273146
MathSciNet review: 273146
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Abstract: We establish necessary conditions for the applicability of Poincaré--Lighthill (or coordinate stretching) perturbation theory to ordinary differential equations. The criteria are simple consequences of a unique modification of the classical theory of coordinate stretching. The usefulness of the new approach and the role of the criteria of applicability are illustrated by means of simple examples.


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DOI: https://doi.org/10.1090/qam/273146
Article copyright: © Copyright 1971 American Mathematical Society


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