Geodesic
Numerical integration of differential equations in the presence of first integrals: observer method
Applicationes Mathematicae, Tome 22 (1993) no. 3, pp. 373-418 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

We introduce a simple and powerful procedure-the observer method-in order to obtain a reliable method of numerical integration over an arbitrary long interval of time for systems of ordinary differential equations having first integrals. This aim is achieved by a modification of the original system such that the level manifold of the first integrals becomes a local attractor. We provide a theoretical justification of this procedure. We report many tests and examples dealing with a large spectrum of systems with different dynamical behaviour. The comparison with standard and symplectic methods of integration is also provided.
DOI : 10.4064/am-22-3-373-418
Keywords: integrable systems, numerical integration, chaotic behaviour, non-integrable systems, ordinary differential equations

Eric Busvelle 1 ; Rachid Kharab 1 ; A. Maciejewski 1 ; Jean-Marie Strelcyn 1

1 
@article{10_4064_am_22_3_373_418,
     author = {Eric Busvelle and Rachid Kharab and A. Maciejewski and Jean-Marie Strelcyn},
     title = {Numerical integration of differential equations in the presence of first integrals: observer method},
     journal = {Applicationes Mathematicae},
     pages = {373--418},
     year = {1993},
     volume = {22},
     number = {3},
     doi = {10.4064/am-22-3-373-418},
     zbl = {0819.34008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am-22-3-373-418/}
}
TY  - JOUR
AU  - Eric Busvelle
AU  - Rachid Kharab
AU  - A. Maciejewski
AU  - Jean-Marie Strelcyn
TI  - Numerical integration of differential equations in the presence of first integrals: observer method
JO  - Applicationes Mathematicae
PY  - 1993
SP  - 373
EP  - 418
VL  - 22
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am-22-3-373-418/
DO  - 10.4064/am-22-3-373-418
LA  - en
ID  - 10_4064_am_22_3_373_418
ER  - 
%0 Journal Article
%A Eric Busvelle
%A Rachid Kharab
%A A. Maciejewski
%A Jean-Marie Strelcyn
%T Numerical integration of differential equations in the presence of first integrals: observer method
%J Applicationes Mathematicae
%D 1993
%P 373-418
%V 22
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/am-22-3-373-418/
%R 10.4064/am-22-3-373-418
%G en
%F 10_4064_am_22_3_373_418
Eric Busvelle; Rachid Kharab; A. Maciejewski; Jean-Marie Strelcyn. Numerical integration of differential equations in the presence of first integrals: observer method. Applicationes Mathematicae, Tome 22 (1993) no. 3, pp. 373-418. doi: 10.4064/am-22-3-373-418

Cité par Sources :