The averaged Lagrangian method

摘要

In this paper we present a new class of symplectic methods, namely variational integrators employing the same integral averaging found in the averaged vector field method. Extensions to higher order are obtained using a collocation approach. The obtained methods are time-symmetric P-series methods.The proposed methods are compared with existing integrators. The tests focus on highly oscillatory problems, like the Fermi-Pasta–Ulam problem.