An adaptive approach to stepsize control in ODE solvers

The efficiency with which the numerical solution of ordinary differential equations can be generated depends to a large extent on the effectiveness of the stepsize adjustment strategy that is used. A new strategy for carrying out this critical task is proposed in this paper. A distinctive feature of its formulation is the incorporation of a mechanism to correct for any persistent deviation of a prescribed solution quality measure from its desired value. The results of an extensive set of numerical experiments are presented to illustrate the superior behavior of the approach with respect to both the widely used locally optimum stepsize strategy and a recently suggested alternate strategy.