On the error control for multistep methods applied to Odes with invariants and Daesin 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 which 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 by the preliminary examples in this paper.