I read that integration algorithms that are not time-reversible tend to be less "stable". Where stable means that the total energy stays constant (is conserved). I'd like to know what it implies if an algorithm is not time-reversible. What would such an algorithm do differently compared to a time-reversible algorithm like the Verlet method? This is not clear to me since Newton's equations of motion are time-reversible (neglecting numerical errors).
Further, I heard a "good" integration algorithm is time-reversible and symplectic. If I understood the term symplectic correctly, an algorithm that is symplectic doesn't necessarily need to be time-reversible, correct? Are there any non-time-reversible algorithms in MDS that are actually used?
Thanks in advance!
