Submission date: 2 March 2020

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.

Mathematics Subject Classification: Primary 34A09, Secondary 34-04, 34A26, 34C08, 34C40, 37C10, 68W30

Keywords and phrases:

Full text arXiv 2003.00740: pdf, ps.