Analyzing the stability behaviour of solutions and their approximations in case of index-$2$ differential-algebraic systems

When integrating regular ordinary differential equations numerically, one tries to match carefully the dynamics of the numerical algorithm with the dynamical behaviour of the true solution. The present paper deals with linear index-$2$ differential-algebraic systems. It is shown how knowledge pertaining to (numerical) regular ordinary differential equations applies provided a certain subspace which is closely related to the tangent space of the constraint manifold remains invariant.