Several numerical methods for solving systems of ordinary differential equations are presented, including multistep methods and single step methods. Particular emphasis is given to the application of these methods to problems in dynamical astronomy.
High order Runge-Kutta methods of the Fehlberg type for first order differential equations and also for second order equations are discussed, as well as other higher order explicit and implicit Runge-Kutta formulations. The new variable-order, variable-step multistep methods and the off-grid methods are mentioned, and the extrapolation methods outlined.