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A note on an expansion formula with application to nonlinear Differential-Algebraic-Equations

  • In [DL] systems of differential polynomials are investigated with respect to properties of Artin approximation type. The key tool in [DL] is an extended version of a formula by Hurwitz [Hu] expressing high order derivatives of an expansion by lower ones. The formula is further refined in [VFZ] to deliver sufficient conditions concerning the existence of power series solutions of scalar algebraic differential equations of order?. In the paper at hand, the main results from [VFZ] are first reproduced and further extended to systems of nonlinear differential algebraic equations. In addition, a simple extension of Tougeron’s implicit function theorem is given in a specific constellation. The results follow from [S1], [S2] where Artin approximation is treated within a Banach space setting, thereby constructing an expansion formula that expresses accurately the required dependency of low and high order derivatives within the system of undetermined coefficients.

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Metadaten
Author:Matthias StiefenhoferORCiD
URN:urn:nbn:de:bvb:859-5812
Place of publication:Kempten
Document Type:Preprint
Language:English
Date of first Publication:2019/12/23
Publishing Institution:Hochschule für angewandte Wissenschaften Kempten
Tag:AlgGeo; Differential polynomials; Hurwitz expansion formula; Separant matrix
Number of pages:15 Seiten
Original Publication / Source:Stiefenhofer, Matthias (2019): A note on an expansion formula with application to nonlinear Differential-Algebraic-Equations, arXiv.org, New York, Cornell University
https://arxiv.org/abs/1912.10735,
https://doi.org/10.48550/arXiv.1912.10735,
Institutes:Fakultät Maschinenbau
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik
5 Naturwissenschaften und Mathematik / 51 Mathematik
Open Access:open_access
Publication Lists:Stiefenhofer, Matthias
Publication reviewed:nicht begutachtet
Licence (German):Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International
Release Date:2021/02/15
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