An error estimator for the numerical solution of DAE's using a special class of one-step methods

Error estimators for Runge-Kutta and Rosenbrock methods to solve semi-explicit problems of index 1 are considered. The basis of these error estimators are asymptotic expansions of the global discretization error. The main. error terms of each of the asymptotic expansions satisfy a linear DAE of index 1, called error-DAE. Using a condition on the principal error function this DAE can be solved for the main error terms. This condition results in practice in further conditions for the defining parameters of the method. Numerical results are presented.