Sharma, HarshBorggaard, Jeffrey T.Patil, MayureshWoolsey, Craig A.2023-12-212023-12-212022-111007-5704https://hdl.handle.net/10919/117260A fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive time-step variational integrators that conserve the energy in addition to being symplectic and momentum-preserving. Their utility, however, is still an open question due to the numerical difficulties associated with solving the discrete governing equations. In this work, we investigate the numerical performance of energy-preserving, adaptive time-step variational integrators. First, we compare the time adaptation and energy performance of the energy-preserving adaptive algorithm with the adaptive variational integrator for Kepler's two-body problem. Second, we apply tools from Lagrangian backward error analysis to investigate numerical stability of the energy-preserving adaptive algorithm. Finally, we consider a simple mechanical system example to illustrate the backward stability of this energy-preserving, adaptive time-step variational integrator.17 page(s)application/pdfenIn CopyrightEnergy-preserving integratorsVariational integratorsAdaptive time-step integratorsBackward stabilityArticle - Refereedhttps://doi.org/10.1016/j.cnsns.2022.106646114Woolsey, Craig [0000-0003-3483-7135]Borggaard, Jeffrey [0000-0002-4023-7841]1878-7274