  A methodology that can generate the optimal coefficients of a numerical
method with the use of an artificial neural network is presented in this work.
The network can be designed to produce a finite difference algorithm that
solves a specific system of ordinary differential equations numerically. The
case we are examining here concerns an explicit two-stage Runge-Kutta method
for the numerical solution of the two-body problem. Following the
implementation of the network, the latter is trained to obtain the optimal
values for the coefficients of the Runge-Kutta method. The comparison of the
new method to others that are well known in the literature proves its
efficiency and demonstrates the capability of the network to provide efficient
algorithms for specific problems.
