Implicit time difference

From Glossary of Meteorology

implicit time difference

A finite-difference approximation in which the terms producing time change are specified at the predicted time level.

The approximation
(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 an implicit time difference approximation to the differential equation df/dt = g(f). Implicit approximations may be more difficult to implement than explicit time differences. For explicit time differences, g(f) would be specified as g(fn) or g(fn - 1). Implicit time differences are relatively more stable and allow larger time steps than explicit time differences.
Compare leapfrog differencing.