Fast computation of power series solutions of systems of differential equations

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 nonlinear case. This extends previous results obtained by Brent and Kung for scalar differential equations of order 1 and 2.

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Alin Bostan, Frédéric Chyzak, François Ollivier, Bruno Salvy, Éric Schost, Alexandre Sedoglavic
• Keywords: Arithmetic Operations, CORR 2006, Education, Ordinary Point, Power Series Solutions