Symplectic integration with floating-point arithmetic and other approximations Original Research Article

There is significant theoretical support for the use of symplectic integrators for the numerical solution of Hamiltonian systems. However, the theory does not apply to practical computations because of the failure to take into account the effects of roundoff errors, and other approximations such as the use of fast N-body solvers and the use of “not fully converged iterations” in implicit or semi-implicit integrators. Very often these effects grow exponentially with time and completely overwhelm the numerical results well before the integration is complete. By means of a simple and inexpensive modification of the integrator, we show that it is possible to maintain a symplectic integration with floating-point arithmetic and other approximations.