Phase lag analysis of variational integrators using interpolation techniques

In the present work we derive higher order variational integrators and combine them with phase lag properties for the numerical integration of systems with oscillatory solutions. The discrete Lagrangian in any time interval is defined as a weighted sum of the evaluation of the continuous Lagrangian at intermediate time nodes. The expressions used for configurations and velocities use linear interpolation, cubic spline interpolation or interpolation via trigonometric functions. The new methods depend on a frequency, which needs to be chosen appropriately. Results show that the energy error of the integration method is decreased for good frequency estimates. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)