Date
2020-06-17Subject
510 Mathematics Implizite DifferentialgleichungGeometrieSingularität <Mathematik>Reelle algebraische GeometrieComputational logicMetadata
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Aufsatz
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.
Citation
In: Mathematics in Computer Science (MCS) Volume 15 / Issue 2 (2020-06-17) , S. 333-352 ; eissn:1661-8289Sponsorship
Gefördert im Rahmen des Projekts DEALCitation
@article{doi:10.17170/kobra-202105203943,
author={Seiler, Werner M. and Seiß, Matthias and Sturm, Thomas},
title={A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations},
journal={Mathematics in Computer Science (MCS)},
year={2020}
}
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2021-05-25T10:29:42Z 2021-05-25T10:29:42Z 2020-06-17 doi:10.17170/kobra-202105203943 http://hdl.handle.net/123456789/12847 Gefördert im Rahmen des Projekts DEAL eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ implicit differential equations geometric singularities vessiot distribution real algebraic computations logic computation 510 A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations Aufsatz 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. open access Seiler, Werner M. Seiß, Matthias Sturm, Thomas doi:10.1007/s11786-020-00485-x Implizite Differentialgleichung Geometrie Singularität <Mathematik> Reelle algebraische Geometrie Computational logic publishedVersion eissn:1661-8289 Issue 2 Mathematics in Computer Science (MCS) 333-352 Volume 15 false
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