Control of step size and order in extrapolation codes

摘要

Extrapolation of the semi-implicit midpoint rule is an effective way to solve stiff initial value problems for a system of ordinary differential equations. The theory of the control of step size and order is advanced by investigating questions not taken up before, providing additional justification for some algorithms, and proposing an alternative to the information theory approach of Deuflhard. An experimental code SIMP implementing the algorithms proposed is shown to be as good as, and in some respects better than, the research code METAN1 of Bader and Deuflhard.