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arXiv · 0705.2127

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

Ali Ayad
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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.

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Ali Ayad. 2007-05-15. On the complexity of solving ordinary differential equations in terms of Puiseux series. https://arxiv.org/abs/0705.2127

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