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

Werner Seiler 1 Matthias Seiss 1 Thomas Sturm 2, 3
2 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
MPII - Max-Planck-Institut für Informatik, Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
3 MOSEL - Proof-oriented development of computer-based systems
LORIA - FM - Department of Formal Methods
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.
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https://hal.archives-ouvertes.fr/hal-02978976
Contributor : Thomas Sturm Connect in order to contact the contributor
Submitted on : Monday, October 26, 2020 - 8:17:38 PM
Last modification on : Saturday, October 16, 2021 - 11:26:09 AM

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  • HAL Id : hal-02978976, version 1
  • ARXIV : 2003.00740

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Werner Seiler, Matthias Seiss, Thomas Sturm. A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations. 2020. ⟨hal-02978976⟩

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