Runge-Kutta Five

5th order Runge-Kutta integrator (fixed-step)

In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which includes the well-known routine called the Euler Method, used in temporal discretization for the approximate solutions of ordinary differential equations. These methods were developed around 1900 by the German mathematicians C. Runge and M. W. Kutta.
Here, integration of the normalized two-body problem from t0 = 0 to t = 86400 for an eccentricity of e = 0.1 is implemented.
Reference:
Boulet, D.L., 1991. Methods of Orbit Determination for the Microcomputer. Willmann-Bell.