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}
}