Abstract
We provide the drawing of the output of dynamical system (Σ), particularly when the output is rough or near instability points. (Σ) being analytical in a neighborhood of the initial state q(0) and described 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 [t i ,t i + 1]0 ≤ i ≤ n − 1, to draw y(t) everywhere as far as possible. At every point t i + 1 we calculate at order k an approximated value of each component q r of the state; on every interval [t i ,t i + 1]0 ≤ i ≤ n − 1 we calculate an approximated output. These computings are obtained from the symbolic expressions of the generating series of q r and y, truncated at order k, specified for t = t i and “evaluated”. A Maple package is built, providing a suitable result for oscillating outputs or near instability points when a Runge-Kutta method is wrong.
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Benmakrouha, F., Hespel, C., Monnier, E. (2012). Generating Series for Drawing the Output of Dynamical Systems. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_11
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DOI: https://doi.org/10.1007/978-3-642-27413-8_11
Publisher Name: Springer, Berlin, Heidelberg
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