Interval Runge-Kutta Methods with Variable Step Sizes

Abstract

In a number of our previous papers we have presented interval versions of Runge-Kutta methods (explicit and implicit) in which the step size was constant. Such an approach has required to choose manually the step size in order to ensure an interval enclosure to the solution with the smallest width. In this paper we propose an algorithm for choosing automatically the step size which guarantees the best (i.e., the tiniest) interval enclosure. This step size is determined with machine accuracy.