An Optimized Fourth Order Runge-Kutta Method

In this paper the order conditions for Runge-Kutta methods are presented based on Butcher's rooted tree theory. A new Runge-Kutta method of order four (MINRK4) is obtained by means of minimizing the error constant. The results of numerical experiments show the competence of the new method in accuracy and efficiency compared with some highly efficient codes in the literature.