Fast computation of power series solutions of systems of differential equations

Alin Bostan 1 Frédéric Chyzak 1 François Ollivier 2, 3 Bruno Salvy 1 Éric Schost 2 Alexandre Sedoglavic 4, 5
1 ALGO - Algorithms
Inria Paris-Rocquencourt
3 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
5 CALFOR - Calcul Formel
LIFL - Laboratoire d'Informatique Fondamentale de Lille
Abstract : We propose new algorithms for the computation of the first N terms of a vector (resp. a basis) of power series solutions of a linear system of differential equations at an ordinary point, using a number of arithmetic operations which is quasi-linear with respect to N. Similar results are also given in the non-linear case. This extends previous results obtained by Brent and Kung for scalar differential equations of order one and two.
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Submitted on : Monday, April 24, 2006 - 10:19:40 PM
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Alin Bostan, Frédéric Chyzak, François Ollivier, Bruno Salvy, Éric Schost, et al.. Fast computation of power series solutions of systems of differential equations. 2007 ACM-SIAM Symposium on Discrete Algorithms, ACM-SIAM, Jan 2007, New Orleans, Louisiana, United States. pp.1012-1021. ⟨inria-00001264⟩

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