Fast computation of power series solutions of systems of differential equations

Details Fast computation of power series solutions of systems of differential equations Fast computation of power series solutions of systems of differential equations

2006-04-25

arxiv.org/abs/cs/0604101v1

Dans 2007 ACM-SIAM Symposium on Discrete Algorithms (2007) 1012--1021

Computer Science

Symbolic Computation

Scientific paper

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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