English

On the complexity of solving ordinary differential equations in terms of Puiseux series

General Mathematics 2007-05-23 v1

Abstract

We prove that the binary complexity of solving ordinary polynomial differential equations in terms of Puiseux series is single exponential in the number of terms in the series. Such a bound was given by Grigoriev [10] for Riccatti differential polynomials associated to ordinary linear differential operators. In this paper, we get the same bound for arbitrary differential polynomials. The algorithm is based on a differential version of the Newton-Puiseux procedure for algebraic equations.

Keywords

Cite

@article{arxiv.0705.2127,
  title  = {On the complexity of solving ordinary differential equations in terms of Puiseux series},
  author = {Ali Ayad},
  journal= {arXiv preprint arXiv:0705.2127},
  year   = {2007}
}