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Theses

Utilisation de la méthode d'équivalence de Cartan dans la construction d'un solveur d'équations différentielles

Abstract : Current ODE-solvers make use of a combination of symmetry methods and classification methods. Classification methods are used when the ODE matches a recognizable pattern (that is, for which a solving method is already implemented), and symmetry methods are reserved for the non-classifiable cases. Using symmetry methods, the solvers first look for the generators of 1-parameter symmetry groups of the given ODE, and then use this information to integrate it, or at least reduce its order. In practice, present solvers are often unable to return closed form solution. The the aim of this thesis is to propose an algorithm for a new ODE-solver, based on Cartan's equivalence method, which should improve the abilities of current solvers to handle second order differential equations. The thesis provides also a theoretical result revealing the relationship between the change of coordinates, that maps the generic equation to a given target equation, and the symmetry pseudo-group of this target.
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https://tel.archives-ouvertes.fr/tel-00264288
Contributor : Raouf Dridi <>
Submitted on : Friday, March 14, 2008 - 7:33:40 PM
Last modification on : Thursday, March 5, 2020 - 6:22:57 PM
Long-term archiving on: : Friday, May 21, 2010 - 12:29:41 AM

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  • HAL Id : tel-00264288, version 1

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Raouf Dridi. Utilisation de la méthode d'équivalence de Cartan dans la construction d'un solveur d'équations différentielles. Mathématiques [math]. Université des Sciences et Technologie de Lille - Lille I, 2007. Français. ⟨tel-00264288⟩

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