Numerical integration

Abstract

On the basis of the structural characterization of index-1 DAEs given in Chapter 4, we analyze how integration methods behave when applied to those DAEs. We consider backward differentiation methods, Runge-Kutta methods and general linear methods. We concentrate on the question of whether a given method which is directly applied to the original DAE passes the wrapping unchanged and is handed over to the so-called inherent explicit ODE. The answer appears not to be a feature of the method, but a property of the DAE formulation. If the subspace accommodating the derivative term is actually time-invariant, then the integration method reaches the inherent explicit ODE unchanged. This makes the integration smooth to the extend to which it may be smooth for explicit ODEs. Otherwise one has to expect additional serious stepsize restrictions.