arXiv subjects

Ali Ayad

Publications and source records attributed to Ali Ayad.

2 recordsLinked to original sources

arXiv2008

A note on the computation of Puiseux series solutions of the Riccatti equation associated with a homogeneous linear ordinary differential equation

We present in this paper a detailed note on the computation of Puiseux series solutions of the Riccatti equation associated with a homogeneous linear ordinary differential equation. This paper is a continuation of [1] which was on the complexity of solving arbitrary ordinary polynomial differential equations in terms of Puiseux series.

math.CA↗

arXiv2007

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

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.

math.GM↗