We present a new type of asymptotic expansions for functions of two variables, the coefficients of which contain functions of one of the variables as well as functions of the quotient of these two variables. These combined asymptotic expansions (cae) are particularly well suited for the description of solutions of singularly perturbed ordinary differential equations in the neighborhood of turning points. The relations with the method of matched asymptotic expansions and with the classical cae used for boundary layers are described. An application to canard solutions is given.
On présente une théorie de développements asymptotiques pour des fonctions de deux variables, combinant à la fois des fonctions d'une des variables et des fonctions du quotient de ces deux variables. Ces développements asymptotiques combinés (dac) sont bien adaptés à la description des solutions d'équations différentielles ordinaires singulièrement perturbées au voisinage de points tournants. Le lien et les différences avec les méthodes de matching et les développements combinés classiques sont décrits. Cette théorie est appliquée à un problème de solutions canard.
Accepted:
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Augustin Fruchard 1; Reinhard Schäfke 2
@article{CRMATH_2010__348_23-24_1273_0,
author = {Augustin Fruchard and Reinhard Sch\"afke},
title = {Composite asymptotic expansions and turning points of singularly perturbed ordinary differential equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {1273--1277},
publisher = {Elsevier},
volume = {348},
number = {23-24},
year = {2010},
doi = {10.1016/j.crma.2010.10.027},
language = {en},
}
TY - JOUR AU - Augustin Fruchard AU - Reinhard Schäfke TI - Composite asymptotic expansions and turning points of singularly perturbed ordinary differential equations JO - Comptes Rendus. Mathématique PY - 2010 SP - 1273 EP - 1277 VL - 348 IS - 23-24 PB - Elsevier DO - 10.1016/j.crma.2010.10.027 LA - en ID - CRMATH_2010__348_23-24_1273_0 ER -
%0 Journal Article %A Augustin Fruchard %A Reinhard Schäfke %T Composite asymptotic expansions and turning points of singularly perturbed ordinary differential equations %J Comptes Rendus. Mathématique %D 2010 %P 1273-1277 %V 348 %N 23-24 %I Elsevier %R 10.1016/j.crma.2010.10.027 %G en %F CRMATH_2010__348_23-24_1273_0
Augustin Fruchard; Reinhard Schäfke. Composite asymptotic expansions and turning points of singularly perturbed ordinary differential equations. Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1273-1277. doi : 10.1016/j.crma.2010.10.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.027/
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