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

Ali Ayad (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Newton-Puiseux polygon

Mots clés: Symbolic computation; Complexity theory; Polynomial differential equations; Puiseux series; Newton-Puiseux polygon.

Domaines: Mathématiques générales [math.GM]

Ali Ayad. On the complexity of solving ordinary differential equations in terms of Puiseux series. 2007. ⟨hal-00146203⟩