Report 1999-12

Numerical integration of differential algebraic systems and invariant manifolds

K. Nipp

Abstract: The dynamics of a differential algebraic equation takes place on a lower dimensional manifold in phase space. Applying a numerical integration scheme, it is natural to ask if and how this geometric property is preserved by the discrete dynamical system. In the index-1 case answers to this question are obtained from the singularly perturbed case treated in [6] for Runge-Kutta methods and in [7] for linear multistep methods. As main result, it is shown that also for Runge-Kutta methods and linear multistep methods applied to an index-2 problem of Hessenberg form there is a (attractive) invariant manifold for the discrete dynamical system and this manifold is close to the manifold of the differential algebraic equation.

Paper: Available as PDF (442 KB) or as hardcopy to order reports@sam.math.ethz.ch.