Differential Algebraic Equations a New Look at the Index G. Le Vey
نویسنده
چکیده
Systems of Diierential-Algebraic Equations (DAE's) have been widely investigated, during the last twenty years, from a numerical point of view. The notion of index has shown to be eecient for the classiication of such systems with respect to the diiculties when trying to solve them with the standard discretization schemes. In this paper, our interest is in the study of formal (\structural") properties of DAE systems : we make the link between the index of a DAE system and general notions coming from the formal theory of PDE's. This interpretation gives new insights for the understanding of DAE's and allows us to give rigorous justiication of manipulations that are of usual practice in this area. Equations dii erentielles alg ebriques Un point de vue nouveau sur la notion d'indice R esum e : Les deux derni eres d ecennies ont vu un grand nombre de travaux porter sur l'ana-lyse num erique des syst emes d' equations dii erentielles alg ebriques (DAE). La notion d'indice s'est progressivement r ev el ee ^ etre un concept important pour caract eriser le degr e de diicult e dans la r esolution num erique de ces syst emes. Nous nous int eressons dans ce travail aux propri et es formelles (\structurelles") des DAE, au moyen d'outils plus g en eraux venant de la th eorie formelle des EDP. Ce cadre permet une d eenition rigoureuse de l'indice qui soit applicable aussi bien aux syst emes sur-d etermin es et ne n ecessite pas la r eduction pr ealable a un syst eme du premier ordre. Plusieurs autres notions, apparaissant dispers ees dans la litt erature, sont replac ees dans ce cadre et ree coivent de ce fait un statut pr ecis. Diierential Algebraic Equations a new look at the index
منابع مشابه
Formal Theory of Differential-algebraic Systems
1994 Abstract. We propose a new approach to diierential-algebraic systems based on the formal theory of partial diierential systems. This results in a new deenition of the index of the system, which is similar to but more general than the one proposed recently by Rabier and Rheinboldt. This index, however, is not related to the numerical diiculty of solving the system, but to the amount of symb...
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تاریخ انتشار 1994