Numerical solution and structural analysis of differential-algebraic equations

Abstract

In the last two decades differential-algebraic equations (DAEs) have become an important branch in numerical analysis. In this Thesis we study them from a new, geometric point of view. The DAE is interpreted as a subset of a jet bundle and its solution are induced by the Cartan distribution on the jet bundle. We also introduce a method to examine and define the structure of a general, polynomial, DAE whose locus is not necessarily a fibred manifold. Also it is shown how some singularities of multibody systems are removed by using the algebraic techniques used in this approach.