RT info:eu-repo/semantics/article
T1 Solving first order autonomous algebraic ordinary differential equations by places
A1 Falkensteiner, Sebastian
A1 Sendra Pons, Juan Rafael
K1 Algebraic autonomous differential equation
K1 Algebraic curve
K1 Local para-metrization
K1 Place
K1 Formal power series solution
K1 Analytic solution
K1 Matemáticas
K1 Mathematics
AB Given a first order autonomous algebraic ordinary differential equation, we present a method for computing formal power series solutions by means of places. We provide an algorithm for computing a full characterization of possible initial values, classified in terms of the number of distinct formal power series solutions extending them. In addition, if a particular initial value is given, we present a second algorithm that computes all the formal power series solutions, up to a suitable degree, corresponding to it. Furthermore, when the ground field is the field of the complex numbers, we prove that the computed formal power series solutions are all convergent in suitable neighborhoods.
PB Springer
SN 1661-8270
YR 2019
FD 2019-12-17
LK http://hdl.handle.net/10017/55321
UL http://hdl.handle.net/10017/55321
LA eng
NO Agencia Estatal de Investigación
DS MINDS@UW
RD 26-abr-2024