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Leapfrog is time reversible because of the symmetric way in which it is defined, unlike the other schemes.
- In Euler, forward and backward steps do not cancel since they use different derivatives at different times.
- In Midpoint, the estimate of the derivative is based on an extrapolation from the left-hand side of the interval. On time reversal, the estimate would be based on the right-hand side, not the same.
- Similarly, RK4 is not time reversible.