On the error control for multistep methods applied to ODEs with invariants and DAEs in multibody dynamics

Abstract:
A modified local error model is developed for numerical integration of ODEs with invariants. The basic idea is to use a commutativity relationship that holds for implicit state-space form methods. A new implicit state-space form predictor is developed from which error estimates can be obtained by predictor-corrector difference: This technique is demonstrated through the preliminary examples in this paper.