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A geometric index reduction method for implicit systems of differential algebraic equations |
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| Authors: | L D’Alfonso G Jeronimo F Ollivier A Sedoglavic P Solernó |
| Affiliation: | aDepartamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina;bDepartamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina;cCONICET, Argentina;dLIX, UMR CNRS–École Polytechnique no 7161, F-91128 Palaiseau, France;eLIFL, UMR CNRS–Université de Lille I no 8022, F-59655 Villeneuve d’Ascq, France |
| Abstract: | This paper deals with the index reduction problem for the class of quasi-regular DAE systems. It is shown that any of these systems can be transformed to a generically equivalent first order DAE system consisting of a single purely algebraic (polynomial) equation plus an under-determined ODE (a differential Kronecker representation) in as many variables as the order of the input system. This can be done by means of a Kronecker-type algorithm with bounded complexity. |
| Keywords: | Implicit systems of Differential Algebraic Equations Index Kronecker algorithm Geometric resolution |
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