New classification techniques for ordinary differential equations

Abstract : The goal of the present paper is to propose an enhanced ordinary differential equation 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 ODEs, that are regarded as well-known, or at least well-studied. The dictionary considered in this article comprises the ODEs 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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Journal of Symbolic Computation, Elsevier, 2009, 44 (7), pp.836 - 851. 〈10.1016/j.jsc.2008.04.010〉
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Raouf Dridi, Michel Petitot. New classification techniques for ordinary differential equations. Journal of Symbolic Computation, Elsevier, 2009, 44 (7), pp.836 - 851. 〈10.1016/j.jsc.2008.04.010〉. 〈inria-00450410〉

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