CONTROL-THEORETIC TECHNIQUES FOR STEPSIZE SELECTION IN IMPLICIT RUNGE-KUTTA METHODS

The problem of stepsize selection in implicit Runge-Kutta schemes is a nalyzed from a feedback control point of view. This approach leads to a better understanding of the relation between stepsize and error. A n ew dynamical model describing this relation is derived. The model is u sed as a basis for a new stepsize selection rule. This rule achieves b etter error control at little extra expense. The properties of the new model and the improved performance of the new error control are demon strated using both analysis and numerical examples.