New classification techniques for ordinary differential equations

• Autores: Raouf Dridi, Michel Petitot
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 44, Nº 7, 2009, págs. 836-851
• Idioma: inglés
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• Resumen

  • 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.