Runge Kutta 8th Order Integration

In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which include 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 Carl Runge and Martin Kutta. Here, integration of the normalized two-body problem from t0 = 0 [s] to t = 3600 [s] for an eccentricity of e = 0.1 is implemented and compared with analytical method.

Reference:
Goddard Trajectory Determination System (GTDS): Mathematical Theory, Goddard Space Flight Center, 1989.