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Chapitre D'ouvrage Année : 2011

Generating series for drawing output of dynamical systems

Résumé

We provide the drawing of the output of dynamical system ( ), particularly when the output is rough or near instability points. ( ) being analytical in a neighborhood of the initial state q(0) and de- scribed by its state equations, its output y(t) in a neighborhood of t = 0 is obtained by \evaluating" its generating series. Our algorithm consists in juxtaposing local approximating outputs on successive time intervals [ti; ti+1]0 i n1, to draw y(t) everywhere as far as possible. At every point ti+1 we calculate at order k an approximated value of each component qr of the state; on every interval [ti; ti+1]0 i n1 we calculate an approximated output. These computings are obtained from the symbolic expressions of the generating series of qr and y, truncated at order k, speci ed for t = ti and \evaluated". A Maple package is built, providing a suitable result for oscillating out- puts or near instability points when a Runge-Kutta method is wrong.
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Dates et versions

hal-00682433 , version 1 (26-03-2012)

Identifiants

  • HAL Id : hal-00682433 , version 1

Citer

Farida Benmakrouha, Christiane Hespel, Edouard Monnier. Generating series for drawing output of dynamical systems. J.-D. Boissonnat et al. Curves and Surfaces 2011LNCS 6920, Springer, Heidelberg, pp.178-192, 2011. ⟨hal-00682433⟩
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