New Runge-Kutta algorithms for numerical simulation in dynamical astronomy

Some new Runge-Kutta and Runge-Kutta-Nystrom algorithms are presented for the solution of ordinary differential equations of the initial value type. The methods are compared with others in integrating the equations of motion of the two body problem and are shown to offer advantages in efficiency. It is also demonstrated that the new methods can be tuned to achieve some measure of global error control.