Stability preserving integration of index-2 DAEs Original Research Article

For linear index-2 DAEs with properly stated leading term we characterize contractive and dissipative flows. We study under which conditions the qualitative properties of the DAE solutions are reflected by the numerical approximations. This is the case if the discretization and the decoupling processes commute. Commutativity is achieved if two subspaces associated with the index-2 DAE are constant; in this case we say that the index-2 DAE is numerically qualified. If both subspaces are time dependent, the problem should be reformulated; in order to avoid numerically equivalent reformulations, a criterion is given. If only one of these subspaces is constant, the problem is in some sense close to a numerically qualified one and thus depending on the problem context, no reformulations are needed. Contractive and dissipative flows induced by the DAE are characterized and results on qualitative properties of the numerical solution are given.