@inproceedings{BCOSSS07,
    author      = {Bostan, Alin and Chyzak, Fr{\'e}d{\'e}ric and Ollivier,
  Fran\c{c}ois and Salvy, Bruno and Schost, {\'E}ric and Sedoglavic,
  Alexandre},
    title       = {Fast computation of power series solutions of systems of
  differential equations},
    pages       = {1012--1021},
    booktitle   = {18th ACM-SIAM Symposium on Discrete Algorithms},
    year        = {2007},
    note        = {New Orleans, January 2007},
    arxiv       = {cs.SC/0604101},
    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.},
}