Fast computation of power series solutions of systems of differential equations
Alin Bostan, Frédéric Chyzak, François Ollivier, Bruno Salvy, Éric Schost, Alexandre Sedoglavic
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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