Geodesic
Puiseux series solutions of ODEs
Electronic journal of differential equations, Tome 2015 (2015)
In this article, we will determine Puiseux series solutions of ordinary polynomial differential equations. We also study the binary complexity of computing such solutions. We will prove that this complexity bound is single exponential in the number of terms in the series. Our algorithm is based on a differential version of the Newton-Puiseux procedure for algebraic equations.
Classification : 12H05, 13F25, 68W30, 68Q25
Keywords: symbolic computations, complexity analysis of algorithms, ordinary polynomial differential equations, formal power series, Newton polygons 
@article{EJDE_2015__2015__a39,
     author = {Ayad,  Ali and Fares,  Ali and Ayyad,  Youssef and Tarraf,  Raafat},
     title = {Puiseux series solutions of {ODEs}},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1328.12016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a39/}
}
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Ayad,  Ali; Fares,  Ali; Ayyad,  Youssef; Tarraf,  Raafat. Puiseux series solutions of ODEs. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a39/