Numerical integration of differential equations in the presence of first integrals: observer method

• Autorzy: Eric Busvelle , Rachid Kharab , A. J. Maciejewski , Jean-Marie Strelcyn
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

integrable systems; numerical integration; chaotic behaviour; non-integrable systems; ordinary differential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1993-1995
• Tom: 22
• Numer: 3
• Strony: 373-418

Daty

wydano

1994

otrzymano

1993-12-15

Twórcy

autor

Eric Busvelle

• Centre de Recherche Shell S.A., Boîte Postale 20, 76530 Grand-Couronne, France

autor

Rachid Kharab

• Département de Mathématiques, Université De Rouen, URA CNRS 1378, 76821 Mont Saint Aignan, France

autor

A. J. Maciejewski

• Institute of Astronomy, Nicholas Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland

autor

Jean-Marie Strelcyn

• Département de Mathématiques, Université De Rouen, URA CNRS 1378, 76821 Mont Saint Aignan, France

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