Goeken-Johnson Sixth-Order Runge-Kutta Method

ABSTRACT In this paper we drive a new sixth-order Runge-Kutta method, depending on the new fifth order Runge-Kutta method of David Goeken and Olin Johnson, the property of this method is that it needs five function evaluations only where the standard method needs six or seven function evaluations, then this method is compared with the new fifth order Runge-Kutta method.