A Runge–Kutta–Nyström (RKN) pair of orders 4(3) is presented in this paper. A test orbit from the Kepler problem is chosen to be integrated for a specific tolerance. Then the two free parameters of the above RKN4(3) family are trained to perform best. Thus a neural network approach is formed and its objective function is minimized using a differential evolution optimization technique. Finally we observe that the produced pair outperforms standard pairs from the literature for the Kepler orbits over a wide range of eccentricities and tolerances.

This content is only available via PDF.
You do not currently have access to this content.