AN ERROR ESTIMATOR FOR THE NUMERICAL-SOLUTION OF DAES 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 erro r. 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 pr incipal error function this DAE can be solved for the main error terms . This condition results in practice in further conditions for the def ining parameters of the method. Numerical results are presented.