Modified order and stepsize strategies in Adams codes

We derive some modifications to the order and stepsize strategies of an Adams multistep code. The objective is to produce smoother and more efficient handling of mildly stiff problems without affecting the codes performance on non-stiff problems. Results are given for the Van der Pol equation (before and after) to show the effect of the changes. We also consider introducing a modified predictor–corrector method, with an enlarged stability region, at low order.