New classification techniques for ordinary differential equations

2007/11/30 by Dridi, Raouf, Petitot, Michel
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0712.0002

Abstract

The goal of the present paper is to propose an enhanced ordinary differential equations solver by exploitation of the powerful equivalence method of Élie Cartan. This solver returns a target equation equivalent to the equation to be solved and the transformation realizing the equivalence. The target ODE is a member of a dictionary of ODE, that are regarded as well-known, or at least well-studied. The dictionary considered in this article are ODE in a book of Kamke. The major advantage of our solver is that the equivalence transformation is obtained without integrating differential equations. We provide also a theoretical contribution revealing the relationship between the change of coordinates that maps two differential equations and their symmetry pseudo-groups.

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