NEURAL NETWORK-BASED DERIVATION OF EFFICIENT HIGH-ORDER RUNGE-KUTTA-NYSTROM PAIRS FOR THE INTEGRATION OF ORBITS

We use a neural network approach to derive a Runge-Kutta-Nystrom pair of orders 8(6) for the integration of orbital problems. We adopt a differential evolution optimization technique to choose the free parameters of the method's family. We train the method to perform optimally in a specific test orbit from the Kepler problem for a specific tolerance. Our measure of efficiency involves the global error and the number of function evaluations. Other orbital problems are solved to test the new pair.