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TitleNew classification techniques for ordinary differential equations
Author(s) Raouf Dridi, Michel Petitot
TypeArticle in Journal
AbstractThe 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.
KeywordsCartanís equivalence method, D -groupoids, ODE-solver
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717108001247
LanguageEnglish
JournalJournal of Symbolic Computation
Volume44
Number7
Pages836 - 851
Year2009
NoteInternational Symposium on Symbolic and Algebraic Computation
Edition0
Translation No
Refereed No
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