RT info:eu-repo/semantics/article
T1 Puiseux Series and Algebraic Solutions of First Order Autonomous AODEs – A MAPLE Package
A1 Boulier, François
A1 Cano Torres, José María
A1 Falkensteiner, Sebastian
A1 Sendra Pons, Juan Rafael
K1 Matemáticas
K1 Maple     Symbolic computation     Algebraic differential equation     Formal Puiseux series solution     Algebraic solution
K1 1201 Álgebra
K1 1204 Geometría
K1 1203 Ciencia de Los Ordenadores
AB 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.
PB Springer Science and Business Media Deutschland GmbH
SN 1865-0929
YR 2021
FD 2021
LK https://uvadoc.uva.es/handle/10324/64971
UL https://uvadoc.uva.es/handle/10324/64971
LA spa
NO Communications in Computer and Information Science Volume 1414, Pages 89 - 1032021 4th Maple Conference, MC 2020 Waterloo2 November 2020through 6 November 2020. Code 262939
NO Producción Científica
DS UVaDOC
RD 23-nov-2024