Electron. J. Diff. Equ., Vol. 2015 (2015), No. 135, pp. 1-7.

Puiseux series solutions of ODEs

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
  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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