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Conference Papers Year : 2007

Fast computation of power series solutions of systems of differential equations

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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Dates and versions

inria-00001264 , version 1 (24-04-2006)

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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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