Ali Ayad, Ali Fares, Youssef Ayyad, Raafat Tarraf
Abstract:
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.
Submitted April 29, 2015. Published May 15, 2015.
Math Subject Classifications: 12H05, 13F25, 68W30, 68Q25.
Key Words: Symbolic computations; complexity analysis of algorithms;
ordinary polynomial differential equations; formal power series;
Newton polygons.
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Ali Ayad Lebanese university, Faculty of sciences, Section 1 Department of mathematics, Hadath, Lebanon email: ali.ayad@ul.edu.lb |
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| Ali Fares Lebanese university, Faculty of sciences, Section 1 Department of mathematics, Hadath, Lebanon email: ali.fares@ul.edu.lb | |
| Youssef Ayyad Lebanese university, Faculty of sciences, Section 1 Department of mathematics, Hadath, Lebanon email: youssef.ayyad@ul.edu.lb | |
| Raafat Tarraf Lebanese university, Faculty of sciences, Section 1 Department of mathematics, Hadath, Lebanon email: raafat.taraf@ul.edu.lb |
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