Solving First Order Autonomous Algebraic Ordinary Differential Equations by Places

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...

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Bibliographic Details
Published in:Mathematics in computer science 2020-06, Vol.14 (2), p.327-337
Main Authors: Falkensteiner, Sebastian, Sendra, J. Rafael
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Committees
Complex numbers
Computation
Computer Science
Differential equations
Episcopal churches
Mathematics
Mathematics and Statistics
Ordinary differential equations
Power series
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Summary: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.
ISSN:1661-8270
1661-8289
DOI:10.1007/s11786-019-00431-6