English

Fast computation of power series solutions of systems of differential equations

Symbolic Computation 2008-05-05 v1

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.

Keywords

Cite

@article{arxiv.cs/0604101,
  title  = {Fast computation of power series solutions of systems of differential equations},
  author = {Alin Bostan and Frédéric Chyzak and François Ollivier and Bruno Salvy and Éric Schost and Alexandre Sedoglavic},
  journal= {arXiv preprint arXiv:cs/0604101},
  year   = {2008}
}