On optimal shooting intervals

We develop an adaptive multiple shooting strategy, which is nearly optimal with respect to cpu time. Since the costs of integration are the most important components in this, we investigate in some detail how the gridpoints are chosen by an adaptive integration routine. We use this information to find out where the shooting points have to be selected. We also show that our final strategy is stable in the sense that rounding errors can be kept below a given tolerance. Finally we pay attention to the question how the need for memory can be minimized.