Fast computation of power series solutions
of systems of differential equations

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

Avril 2006

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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