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

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

2007-05-15

arxiv.org/abs/0705.2127v1

Mathematics

General Mathematics

Scientific paper

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.

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