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Fast computation of power series solutions of systems of differential equations

Alin Bostan·Frédéric Chyzak·François Ollivier·Bruno Salvy·Éric Schost·Alexandre Sedoglavic
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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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Alin Bostan, Frédéric Chyzak, François Ollivier, Bruno Salvy, Éric Schost, Alexandre Sedoglavic. 2006-04-25. Fast computation of power series solutions of systems of differential equations. https://arxiv.org/abs/cs/0604101

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