A trigonometrically fitted Runge-Kutta method for the numerical solution of orbital problems

We are presenting a new trigonometrically fitted explicit Runge-Kutta method of fifth algebraic order. The method is an extended form of a classical RK method of Fehlberg, in the sense that we use an extra parameter for each stage of the method, which is multiplied to the initial value yn, and it is used in the process of trigonometrical fitting. The method's efficiency is measured while integrating well known orbital problems and in some cases it is extremely higher compared to classical methods.