On fifth order Runge-Kutta methods

A 6 stage Runge-Kutta method is derived with the property that its order is 5 when used to solve a scalar differential equation but only 4 when used to solve a general system of differential equations. The existence of such a method underlines the necessity of carrying out theoretical analyses in a vector valued setting rather than in a one-dimensional setting as in the work of Kutta and some more recent authors.This research was supported by the New Zealand Foundation for Research, Science and Technology