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
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: We establish necessary conditions for the applicability of PoincarĂ©âLighthill (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.
H. PoincarĂ©, Les mĂ©thodes nouvelles de la mecanique celeste, vol. 1, GauthierâVillars, Paris, 1892; reprint, Dover, New York, 1957
- M. J. Lighthill, A technique for rendering approximate solutions to physical problems uniformly valid, Philos. Mag. (7) 40 (1949), 1179â1201. MR 33941
- Peter D. Usher, Coordinate stretching and interface location. II. A new ${\rm PL}$ expansion, J. Comput. Phys. 3 (1968/69), 29â39. MR 261114, DOI https://doi.org/10.1016/0021-9991%2868%2990003-x
- H. S. Tsien, The PoincarĂ©-Lighthill-Kuo method, Advances in applied mechanics, vol. IV, Academic Press Inc., New York, N.Y., 1956, pp. 281â349. MR 0079929
- Wolfgang Wasow, On the convergence of an approximation method of M. J. Lighthill, J. Rational Mech. Anal. 4 (1955), 751â767. MR 73785, DOI https://doi.org/10.1512/iumj.1955.4.54029
- Craig Comstock, On Lighthillâs method of strained coordinates, SIAM J. Appl. Math. 16 (1968), 596â602. MR 227559, DOI https://doi.org/10.1137/0116048
- Nicolas Minorsky, Nonlinear oscillations, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1962. MR 0137891
H. PoincarĂ©, Les mĂ©thodes nouvelles de la mecanique celeste, vol. 1, GauthierâVillars, Paris, 1892; reprint, Dover, New York, 1957
M. J. Lighthill, A technique for rendering approximate solutions to physical problems uniformly valid, Philos. Mag. (7) 40, 1179â1201 (1949)
P. D. Usher, Coordinate stretching and interface location II, a new PL expansion, J. Computational phys. 3, 29 (1968)
H. S. Tsien, The PoincarĂ©âLighthillâKuo method, Advances in Appl. Mech., vol.4, Academic Press New York, 1956, pp. 281â349
W. A. Wasow, On the convergence of an approximation method of M. J. Lighthill, J. Rational Mech. Anal. 4, 751â767 (1955)
C. Comstock, On Lighthillâs method of strained coordinates, SIAM J. Appl. Math. 16, 596â602 (1968)
N. Minorsky, Nonlinear oscillations, Van Nostrand, Princeton, N. J., 1962
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
34.53
Retrieve articles in all journals
with MSC:
34.53
Additional Information
Article copyright:
© Copyright 1971
American Mathematical Society