Skip to Main content Skip to Navigation
New interface
Journal articles

A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations

Abstract : We discuss the effective computation of geometric singularities of implicit ordinary differential equations over the real numbers using methods from logic. Via the Vessiot theory of differential equations, geometric singularities can be characterised as points where the behaviour of a certain linear system of equations changes. These points can be discovered using a specifically adapted parametric generalisation of Gaussian elimination combined with heuristic simplification techniques and real quantifier elimination methods. We demonstrate the relevance and applicability of our approach with computational experiments using a prototypical implementation in Reduce .
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03438167
Contributor : Thomas Sturm Connect in order to contact the contributor
Submitted on : Sunday, November 21, 2021 - 7:31:15 AM
Last modification on : Friday, July 8, 2022 - 10:06:23 AM
Long-term archiving on: : Tuesday, February 22, 2022 - 6:56:48 PM

File

Seiler2021_Article_ALogicBased...
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

Collections

Citation

Werner M Seiler, Matthias Seiss, Thomas Sturm. A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations. Mathematics in Computer Science, 2021, 15 (2), pp.333-352. ⟨10.1007/s11786-020-00485-x⟩. ⟨hal-03438167⟩

Share

Metrics

Record views

17

Files downloads

23