Geodesic
Numerical integration of differential equations in the presence of first integrals: observer method
Applicationes Mathematicae, Tome 22 (1993) no. 3, pp. 373-418.

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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 
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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. http://geodesic.mathdoc.fr/articles/10.4064/am-22-3-373-418/

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