On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations

Sebastian Falkensteiner; Yi Zhang; Thieu N. Vo

doi:10.1007/s00009-022-01984-w

On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations

Sebastian Falkensteiner, Yi Zhang, Thieu N. Vo

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

1 Citation (SciVal)

Abstract

Given an algebraic ordinary differential equation (AODE), we propose a computational method to determine when a truncated power series can be extended to a formal power series solution. If a certain regularity condition on the given AODE or on the initial values is fulfilled, we compute all of the solutions. Moreover, when the existence is confirmed, we present the algebraic structure of the set of all formal power series solutions.

Original language	English
Article number	74
Journal	Mediterranean Journal of Mathematics
Volume	19
Issue number	2
Early online date	22 Feb 2022
DOIs	https://doi.org/10.1007/s00009-022-01984-w
Publication status	Published - 30 Apr 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Acknowledgements

The authors would like to thank Gleb Pogudin and François Boulier for useful discussions.

Keywords

algebraic differential equation
Formal power series

ASJC Scopus subject areas

General Mathematics

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10.1007/s00009-022-01984-w

Cite this

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abstract = "Given an algebraic ordinary differential equation (AODE), we propose a computational method to determine when a truncated power series can be extended to a formal power series solution. If a certain regularity condition on the given AODE or on the initial values is fulfilled, we compute all of the solutions. Moreover, when the existence is confirmed, we present the algebraic structure of the set of all formal power series solutions.",

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On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations

Abstract

Bibliographical note

Acknowledgements

Keywords

ASJC Scopus subject areas

Access to Document

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