Energy conserving and dissipative time finite element schemes for N-body stiff problems

Petrov–Galerkin finite element method is adopted to develop a family of temporal integrators, which preserves the feature of energy conservation or numerical dissipation for non-linear N-body dynamical systems. This leads to an enhancement of numerical stability and the integrators may therefore offer some advantage for the numerical solution of stiff systems in long-term simulations. Dynamically tuneable numerical integration is exploited to improve the accuracy of the time-stepping schemes. Representative simulations for simple non-linear systems show the performance of the schemes in controlling over or damping out unresolved high frequencies