Allgemeine nichtlineare Stabilitätsgleichungen für gerade Stäbe und ihre Anwendung auf kinetische Kippprobleme

Differential algebraic equations (DAEs) are implicit systems of ordinary differential equations F(y',y,t) = 0 for which the Jacobian Fy' is always singular. DAEs arise in many applications and a variety of numerical methods have been developed for solving DAEs. While many of these methods are very useful, almost all of them either require the DAE to have special structure, only work for DAEs of low index, or do not preserve constraints. In this paper we discuss the progress, and remaining difficulties, in the development of a family of constraint preserving numerical integrators for unstructured higher index DAEs. The first half of the paper concerns reduced computational effort. The second half explains some of the robustness of the iterations that has been observed.