Efficiency comparisons of methods for integrating ODEs

AbstractConsiderable work has been done comparing the relative efficiencies of linear multi-step, Runge-Kutta, and extrapolation methods within their respective classes. However, efficiency comparisons between these classes have been relegated to numerical case studies, which can be misleading because they depend on a small set of test problems and particular implementations of the methods. In this paper a unified way of comparing efficiency is presented that makes it possible to assess theoretically the relative efficiencies of methods from the different classes