Methods of numerical integration applied to a system having trivial function evaluations

Abstract

A study has been made to determine which methods of numerical integration require the least computation time for a given amount of truncation error when applied to a particular system of ordinary differential equations where function evaluations are relatively trivial. Recent methods due to Butcher and Gear are compared with classic Runge-Kutta, Kutta-Nyström and Adams methods. Some of the newer one-step methods due to Butcher are found to be slightly superior, but no one method is found to have any great advantage over the others in the application to this particular problem.