Oscillateurs harmoniques faiblement perturbés : l'algorithme numérique des «pas de géants»

Jacqueline Boujot; Alain Pham Ngoc Dinh; Jean-Pierre Veyrier

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1980)

  • Volume: 14, Issue: 1, page 3-23
  • ISSN: 0764-583X

How to cite

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Boujot, Jacqueline, Pham Ngoc Dinh, Alain, and Veyrier, Jean-Pierre. "Oscillateurs harmoniques faiblement perturbés : l'algorithme numérique des «pas de géants»." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 14.1 (1980): 3-23. <http://eudml.org/doc/193350>.

@article{Boujot1980,
author = {Boujot, Jacqueline, Pham Ngoc Dinh, Alain, Veyrier, Jean-Pierre},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {giant step method; slightly perturbed harmonic oscillator; one-step method; principle of the asymptotic expansions; convergence; consistency and stability conditions; Krylov-Bogolioubov; Runge-Kutta},
language = {fre},
number = {1},
pages = {3-23},
publisher = {Dunod},
title = {Oscillateurs harmoniques faiblement perturbés : l'algorithme numérique des «pas de géants»},
url = {http://eudml.org/doc/193350},
volume = {14},
year = {1980},
}

TY - JOUR
AU - Boujot, Jacqueline
AU - Pham Ngoc Dinh, Alain
AU - Veyrier, Jean-Pierre
TI - Oscillateurs harmoniques faiblement perturbés : l'algorithme numérique des «pas de géants»
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1980
PB - Dunod
VL - 14
IS - 1
SP - 3
EP - 23
LA - fre
KW - giant step method; slightly perturbed harmonic oscillator; one-step method; principle of the asymptotic expansions; convergence; consistency and stability conditions; Krylov-Bogolioubov; Runge-Kutta
UR - http://eudml.org/doc/193350
ER -

References

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  1. 1 M ROSEAU, Vibrations non linéaires et théorie de la stabilité, Springer-Verlag, 1966 Zbl0135.30603MR196987
  2. 2 N BOGOLIUBOV et I MITROPOLSKI, Les méthodes asymptotiques en théorie des oscillations non linéaires, Gauthier-Villars, Pans, 1959 Zbl0247.34004
  3. 3 J KEVORKIAN, The Two Variable Expansion Procedure for the Approximate Solution of Certain Non Linear Differential Equations, Lectures Appl Math , part III, A M S , 1966 Zbl0156.16502
  4. 4 P HENRICI, Discrete Variable Methods in Ordinary Differential Equations, J Wiley, 1962 Zbl0112.34901MR135729
  5. 5 M R FEIX A NADEAU et J P VEYRIER, Numerical Algebraic Method «The giant step method», 4e Colloque international sur les methodes avancées de calcul en physique théorique, Saint-Maximim, 1977 
  6. 6 J BOUJOT et A PHAM, C R Acad, Sc , t 286, série A, 1978, p 1063-1066 Zbl0375.65037MR474157
  7. 7 J P VEYRIER, La méthode des pas de géants Application à l'équation de Duffing, Thèse de 3e cycle, Université d'Orléans, juin 1977 
  8. 8 H KABAKOV, A Perturbation Procedure for Weakly Coupled Oscillators, Int J Nonlinear Mechanics, vol 7, 1972, p 125-137 Zbl0238.70018

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