STABILITY OF NUMERICAL-METHODS FOR DIFFERENTIAL-ALGEBRAIC EQUATIONS OF HIGHER INDEX

The solution of higher-index differential-algebraic systems does not depend continuously on perturbations of the algebraic part. Small errors that arise in the discretization of these systems can be amplified during integration and may result in very large errors in the numerical solution. For systems of index 2 we give bounds for the influence of perturbations on the analytical and the numerical solution that is computed by implicit Runge-Kutta methods. These bounds motivate a modification of the numerical method to make it more robust against errors arising in the implementation on a computer.