Necessary Conditions for Applicability of Poincare-Lighthill Perturbation Theory

Summary. We establish necessary conditions for the applicability of Poincaré Ligh thill (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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Work Title Necessary Conditions for Applicability of Poincare-Lighthill Perturbation Theory
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Open Access
Creators
  1. Peter D. Usher
Keyword
  1. Poincare
  2. Lighthill
  3. Perturbation
  4. Coordinate stretching
License CC BY 4.0 (Attribution)
Work Type Article
Publisher
  1. Quarterly of Applied Mathematics
Publication Date January 1971
Subject
  1. Applied Mathematics
Related URLs
Deposited May 06, 2024

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Version 1
published

  • Created
  • Updated
  • Updated Description, Publication Date Show Changes
    Description
    • Summary. We establish necessary conditions for the applicability of Poincaré Ligh thill (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.
    Publication Date
    • 1971-01
  • Added Creator Peter D. Usher
  • Added Necessary Conditions for applicability.pdf
  • Updated Keyword, Subject, License Show Changes
    Keyword
    • Poincare, Lighthill, Perturbation, coordinate stretching
    Subject
    • Applied Mathematics
    License
    • https://creativecommons.org/licenses/by/4.0/
  • Published
  • Updated
  • Updated Keyword, Publisher, Related URLs Show Changes
    Keyword
    • Poincare, Lighthill, Perturbation, coordinate stretching
    • Poincare, Lighthill, Perturbation, Coordinate stretching
    Publisher
    • Quarterly of Applied Mathematics
    Related URLs
    • https://www.jstor.org/stable/43636170