A comparison of some global methods for solving two-point boundary value problems

摘要

A numerical comparison is made between three codes which implement global methods for solving two-point boundary value problems. The codes compared are a collocation method, COLSYS, a deferred correction method, PASVA 3, and a deferred correction method based on mono-implicit Runge-Kutta formulae, HAGRON. Although the difficulty of conducting a fair comparison of complex codes is widely recognised it is nevertheless of great practical importance to try to gauge the relative performance of different codes and the three codes considered in this paper are particularly appropriate for numerical comparison. By choosing a test set which includes both smooth and increasingly stiff problems some interesting characteristics of the codes are noted and some recommendations regarding their use are made.