Extended simulations of non-linear dynamical systems, with or without non-conservative forces, are known to benefit from the preservation of their differential geometric structures. Geometric numerical integrators are ideally suited for such simulations. It has been common to design such geometric numerical integrators based on either previous knowledge of classical numerical integration algorithms, or approximate solutions to the Hamilton--Jacobi equation for transformations near the identity. There is, however, a different approach that bypasses many of the difficulties inherent in the design of higher-order versions of these geometric numerical integrators. It relies on the discretization of the action, from which one derives the numerical algorithms in a straightforward manner. These variational integrators conserve the differential geometric structure of the phase flow automatically.

A freely available Maple package named VarInt is presented that is able to generate variational integrators systematically to arbitrary order based on either built-in quadrature formulae or user-supplied requirements. Some of these variational integrators correspond to well-known classes of geometric numerical algorithms, such as the symplectic partitioned Runge--Kutta and Lobatto IIIA/IIIB methods. However, few variational integrators have been reported that lie outside of the standard classification, although VarInt is certainly not restricted to it.