Can convert Euler's method to a symplectic integrator utilizing v_{n+1} when computing x_{n+1}. That said although such integrators are widely used (usually of

Can convert Euler's method to a symplectic integrator utilizing v_{n+1} when computing x_{n+1}. That said although such integrators are widely used (usually of higher order than Euler's) in celestial mechanics, one is not restricted to them. For example Bulirsch-Stoer is also very used even if it isn't symplectic because remains accurate (energy error very low) even on long integrations.