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.
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): | ![]() |
Release Date: | 2021/02/15 |