Fast computation of power series solutions of systems of differential equations

Alin Bostan; Frédéric Chyzak; François Ollivier; Bruno Salvy; Éric Schost; Alexandre Sedoglavic

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

2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

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

4 LIFL - Laboratoire d'Informatique Fondamentale de Lille

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.

Document type :

Conference papers

Domain :

Computer Science [cs] / Symbolic Computation [cs.SC]

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https://hal.inria.fr/inria-00001264
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Submitted on : Monday, April 24, 2006 - 10:19:40 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:27 PM
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Fast computation of power series solutions of systems of differential equations

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Fast computation of power series solutions of systems of differential equations

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