Embedding Method by Real Numerical Algebraic Geometry for Structurally Unamenable DifferentialAlgebraic Equations
Abstract
Existing structural analysis methods may fail to find all hidden constraints for a system of differentialalgebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for polynomial systems of differentialalgebraic equations, numerical methods are given to solve such cases using numerical real algebraic geometry. First, we propose an embedding method that for a given real analytic system constructs an equivalent system with a fullrank Jacobian matrix. Secondly, we introduce a witness point method, which can help to detect degeneration on all components of constraints of such systems. Thirdly, the two methods above lead to a numerical global structural analysis method for structurally unamenable differentialalgebraic equations on all components of constraints.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 DOI:
 10.48550/arXiv.2111.08160
 arXiv:
 arXiv:2111.08160
 Bibcode:
 2021arXiv211108160Y
 Keywords:

 Mathematics  Numerical Analysis;
 Mathematics  Dynamical Systems
 EPrint:
 27 pages, 5 figures,3 tables