On the change of step size in multistep codes

In this paper the effect of changing step size on the local discretization error of BDF and Adams type methods is considered. According to Shampine and Bogacki the usual assumption for variable step size multistep methods of orderp, that the local discretization error changes by ^p+1 as the step size changes by a factor of , is incorrect and may lead to unreliability in step size selection algorithms. Here, by using the true expression of the local discretization error for variable step size BDF-, Adams- and FLC methods, new algorithms for step size control are proposed. It is shown that the new algorithms are more accurate and reliable than those employed in usual codes. to confirm the advantages of the new algorithms some numerical experiments based on a modified version of EPISODE are presented.