Solving First Order Autonomous Algebraic Ordinary Differential Equations\n by Places

2018/03/13 by Sebastian Falkensteiner, Falkensteiner, Sebastian, J. Rafael Sendra +1
Computer Science · Mathematics · #Advanced Database Systems and Queries #FOS: Computer and information sciences #Numerical methods for differential equations #Polynomial and algebraic computation #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.1803.04731

openalex publication_date 2018/03/13 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Given a first-order autonomous algebraic ordinary differential equation, we\npresent a method for computing formal power series solutions by means of\nplaces. We provide an algorithm for computing a full characterization of\npossible initial values, classified in terms of the number of distinct formal\npower series solutions extending them. In addition, if a particular initial\nvalue is given, we present a second algorithm that computes all the formal\npower series solutions, up to a suitable degree, corresponding to it.\nFurthermore, when the ground field is the field of the complex numbers, we\nprove that the computed formal power series solutions are all convergent in\nsuitable neighborhoods.\n

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