The stabilization of linear multistep methods for constrained mechanical systems Original Research Article

Linear multistep methods from ODE theory may be applied straightforwardly to index-2 DAEs in Hessenberg form if they are strictly stable at infinity (Hairer and Wanner, 1996, Theorem VII.3.6). This condition is very restrictive and excludes, e.g., all higher order Adams methods. In the paper we present an alternative way to apply implicit linear multistep methods to index-2 systems. The convergence of these partitioned linear multistep methods is guaranteed whenever the underlying ODE method is convergent with order p ≥ 3. We discuss the new approach in detail for the application to model equations of constrained mechanical systems. The theoretical results are illustrated by a numerical comparison of multistep methods for index-2 DAEs in Hessenberg form.