Numerical integration of differential equations in the presence of first integrals: observer method
Eric Busvelle; Rachid Kharab; A. Maciejewski; Jean-Marie Strelcyn
Applicationes Mathematicae (1994)
- Volume: 22, Issue: 3, page 373-418
- ISSN: 1233-7234
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topBusvelle, Eric, et al. "Numerical integration of differential equations in the presence of first integrals: observer method." Applicationes Mathematicae 22.3 (1994): 373-418. <http://eudml.org/doc/219103>.
@article{Busvelle1994,
abstract = {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.},
author = {Busvelle, Eric, Kharab, Rachid, Maciejewski, A., Strelcyn, Jean-Marie},
journal = {Applicationes Mathematicae},
keywords = {integrable systems; numerical integration; chaotic behaviour; non-integrable systems; ordinary differential equations; Hamiltonian systems; numerical solution; first integrals; observer method; local attractor; Kepler problem; Gavrilov-Shil'nikov; Anosov flow; symplectic integrators},
language = {eng},
number = {3},
pages = {373-418},
title = {Numerical integration of differential equations in the presence of first integrals: observer method},
url = {http://eudml.org/doc/219103},
volume = {22},
year = {1994},
}
TY - JOUR
AU - Busvelle, Eric
AU - Kharab, Rachid
AU - Maciejewski, A.
AU - Strelcyn, Jean-Marie
TI - Numerical integration of differential equations in the presence of first integrals: observer method
JO - Applicationes Mathematicae
PY - 1994
VL - 22
IS - 3
SP - 373
EP - 418
AB - 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.
LA - eng
KW - integrable systems; numerical integration; chaotic behaviour; non-integrable systems; ordinary differential equations; Hamiltonian systems; numerical solution; first integrals; observer method; local attractor; Kepler problem; Gavrilov-Shil'nikov; Anosov flow; symplectic integrators
UR - http://eudml.org/doc/219103
ER -
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