Error estimators for stiff differential equations

When solving ordinary differential equations numerically, the local error is estimated at each step. In the classical situation of ‘small’ step sizes, it is clear what is required of the error estimators. Stiff problems are solved with ‘large’ step sizes. The quality of error estimators is studied in this situatuion, and it is shown how to modify unsatisfactory estimators so as to improve them greatly. Several formulas from the literature are treated as examples.