Family of higher order exponential variational integrators for split potential systems

In the present work, we derive a family of higher order exponential variational integrators for the numerical integration of systems containing slow and fast potential forces. To increase the order of variational integrators, first the discrete Lagrangian in a time interval is defined as a weighted sum of the evaluation of the continuous Lagrangian at intermediate time nodes while expressions for configurations and velocities are obtained using interpolating functions that can depend on free parameters. Secondly, in order to choose those parameters appropriately, exponential integration techniques are embedded. When the potential can be split into a fast and a slow component, we use different quadrature rules for the approximation of the different parts in the discrete action. Finally, we study the behavior of this family of integrators in numerical tests.