2 research outputs found
New classification techniques for ordinary differential equations
The goal of the present paper is to propose an enhanced ordinary differential
equations solver by exploitation of the powerful equivalence method of \'Elie
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.Comment: This JSC journal version of the ISSAC07 pape