Fast computation of power series solutions of systems of differential equations
<|reference_start|>Fast computation of power series solutions of systems of differential equations: 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.<|reference_end|>
@article{bostan2006fast,
    title={Fast computation of power series solutions of systems of differential
  equations},
    author={Alin Bostan (INRIA Rocquencourt), Fr'ed'eric Chyzak (INRIA
  Rocquencourt), Franc{c}ois Ollivier (LIX), Bruno Salvy (INRIA Rocquencourt),
  'Eric Schost (LIX), Alexandre Sedoglavic (LIFL)},
    journal={Dans 2007 ACM-SIAM Symposium on Discrete Algorithms (2007)
  1012--1021},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0604101},
    primaryClass={cs.SC}
}