## Answer: Leapfrog is

*time reversible*.## Suppose we step back from (

*ti*+1,*xi*+1,*vi*+3/2) to (*ti*,*xi*,*vi*+1/2). Applying the algorithm:*vi*+1/2 =*vi*+3/2 +*f*(*xi*+1)(-*t*)*xi*=*xi*+1 +*vi*+1/2(-t)- These are precisely the steps (in reverse) that we took to advance the system in the first place!

- Hence if we Leapfrog forward in time, then reverse to
*t*= 0, we're back to where we started,*precisely*.