Runge–Kutta Pairs of Orders 6(5) with Coefficients Trained to Perform Best on Classical Orbits

We consider a family of explicit Runge–Kutta pairs orders six and five without any additional property (reduced truncation errors, Hamiltonian preservation, symplecticness, etc.). This offers parameters that someone chooses freely. Then, we train them in order for the presented method to furnish best results on couple Kepler orbits, certain interval tolerance. Consequently, observe an efficient performance wide range orbital problems (i.e., variety eccentricities, perturbed with various disturbances, Arenstorf Pleiades). About 1.8 digits accuracy is gained average over conventional pairs, which truly remarkable methods coming from same order.