Fast computation of power series solutions of systems of differential equations

Authors:
A. Bostan;F. Chyzak;F. Ollivier;B. Salvy;É. Schost;A. Sedoglavic
Affiliations:
ALGO, Inria Rocquencourt, Le Chesnay, France;ALGO, Inria Rocquencourt, Le Chesnay, France;LIX, École polytechnique, Palaiseau, France;ALGO, Inria Rocquencourt, Le Chesnay, France;LIX, École polytechnique, Palaiseau, France;LIFL, Université Lille I, Villeneuve d'Ascq, France
Venue:
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2007

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Abstract

We propose algorithms for the computation of the first N terms of a vector (or a full basis) of power series solutions of a linear system of differential equations at an ordinary point, using a number of arithmetic operations that 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 1 and 2.