Differential algebraic systems anew Original Research Article

It is proposed to figure out the leading term in differential algebraic systems more precisely. Low index linear systems with those properly stated leading terms are considered in detail. In particular, it is asked whether a numerical integration method applied to the original system reaches the inherent regular ODE without conservation, i.e., whether the discretization and the decoupling commute in some sense. In general one cannot expect this commutativity so that additional difficulties like strong stepsize restrictions may arise. Moreover, abstract differential algebraic equations in infinite-dimensional Hilbert spaces are introduced, and the index notion is generalized to those equations. In particular, partial differential algebraic equations are considered in this abstract formulation.