The involutive form of a "higher index" DAE

Teijo Arponen (Helsinki Univ. of Technology, Espoo, Finland)

We present an algorithm to study the structure of polynomial DAEs.  Although
there are already several such algorithms, we argue that they lack certain
properties we consider important.  Our motivation is to get an algebraic analog
to the geometrical approach to DAEs developed by prof. J. Tuomela.  We discuss
about the needed properties of the algorithm and shortly compare it to other
approaches in literature.  Usually DAEs are studied by people who work either
on numerics or on symbolic computation, but not both.  We try to mix these: for
a given DAE, by using symbolic computation we achieve a formulation which is
suitable for doing numerical computations, in the sense that the biggest
problems (drift-off and instability) in DAE numerics are avoided.