Runge–Kutta Pairs of Orders 5(4) Trained to Best Address Keplerian Type Orbits

The derivation of Runge–Kutta pairs orders five and four that effectively uses six stages per step is considered. coefficients provided by such a method are 27 have to satisfy system 25 nonlinear equations. Traditionally, various solutions been tried. Each these makes use some simplified assumptions offers different families methods. Here, we make the most celebrated family appear in literature, where may as last stage first function evaluation from next (FSAL property). under consideration has advantage being solved explicitly. Actually, arrive at subsystem all found with respect free parameters. These parameters adjusted (trained) order deliver pair outperforms other similar 5(4) Keplerian type orbits, e.g., Kepler, perturbed Arenstorf orbit or Pleiades. training differential evolution technique. finally proposed remarkable performance on average more than digit accuracy variety orbits.