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

Tom 22 / 1994

Eric Busvelle, Rachid Kharab, A. Maciejewski, Jean-Marie Strelcyn Applicationes Mathematicae 22 (1994), 373-418 DOI: 10.4064/am-22-3-373-418


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.


  • Eric Busvelle
  • Rachid Kharab
  • A. Maciejewski
  • Jean-Marie Strelcyn

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