Leapfrog differencing

From Glossary of Meteorology

leapfrog differencing

A finite-difference approximation to a time evolution equation in which the time derivative is approximated with values one time step before and one time step ahead of the values that specify other terms of the equation.

The scheme (fn + 1 - fn - 1)/2Δt = g(fn) (where superscript n denotes a point in time, separated by step Δt from the prior [n - 1] and subsequent [n + 1] discrete time levels) is a leapfrog approximation to the differential equation df/dt = g(f).
Compare implicit time difference.