Single and multiple processor performance of a family of stepsize adjustment procedures for ODE solvers.

Abstract

The efficiency with which the numerical solution of ordinary differential equations (ODE) can be generated depends to a large extent on the effectiveness of the stepsize adjustment strategy that is used. In this thesis the relative performance of a family of stepsize adjustment strategies is examined. Included in this family is a new strategy. 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 evaluation of the various strategies is undertaken through an extensive set of numerical experiments which use both single processor and multiple processor ODE solution procedures.