Puiseux Series and Algebraic Solutions of First Order Autonomous AODEs -- A MAPLE Package

Boulier, Francois; Cano, Jose; Falkensteiner, Sebastian; Sendra, Rafael

Document type :

Autre communication scientifique (congrès sans actes - poster - séminaire...): Communication dans un congrès avec actes

Title :

Puiseux Series and Algebraic Solutions of First Order Autonomous AODEs -- A MAPLE Package

Author(s) :

Boulier, Francois [Auteur]

Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Cano, Jose [Auteur]
Universidad de Valladolid [Valladolid] [UVa]
Falkensteiner, Sebastian [Auteur]
Research Institute for Symbolic Computation [RISC]
Sendra, Rafael [Auteur]
Universidad de Alcalá - University of Alcalá [UAH]

Conference title :

Proceedings of the Maple Conference 2020

City :

Waterloo

Country :

Canada

Start date of the conference :

2020-11-02

Publication date :

2021

HAL domain(s) :

Informatique [cs]/Calcul formel [cs.SC]

English abstract : [en]

There exist several methods for computing exact solutions of algebraic differential equations. Most of the methods, however, do not ensure existence and uniqueness of the solutions and might fail after several steps, or ...
Show more >There exist several methods for computing exact solutions of algebraic differential equations. Most of the methods, however, do not ensure existence and uniqueness of the solutions and might fail after several steps, or are restricted to linear equations. The authors have presented in previous works a method to overcome this problem for autonomous first order algebraic ordinary differential equations and formal Puiseux series solutions and algebraic solutions. In the first case, all solutions can uniquely be represented by a sufficiently large truncation and in the latter case by its minimal polynomial. The main contribution of this paper is the implementation, in a MAPLE-package named FirstOrderSolve, of the algorithmic ideas presented therein. More precisely, all formal Puiseux series and algebraic solutions, including the generic and singular solutions, are computed and described uniquely. The computation strategy is to reduce the given differential equation to a simpler one by using local parametrizations and the already known degree bounds.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Méthodes symboliques pour les réseaux biologiques

Collections :