English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Paper

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

MPS-Authors
/persons/resource/persons73108

Sturm,  Thomas
Automation of Logic, MPI for Informatics, Max Planck Society;

External Ressource
No external resources are shared
Fulltext (public)

arXiv:2003.00740.pdf
(Preprint), 890KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Seiler, W. M., Seiss, M., & Sturm, T. (2020). A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations. Retrieved from https://arxiv.org/abs/2003.00740.


Cite as: http://hdl.handle.net/21.11116/0000-0007-7A09-7
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.