Semi-implicit method

From Glossary of Meteorology

semi-implicit method

A finite difference approximation in which some terms producing time change are specified at an earlier time level.

The approximation (fn + 1 - fn - 1)/2Δt = g(fn + 1) + h(fn) (where superscript n denotes a point in time, separated by step Δt from the prior [n - 1] and subsequent [n + 1] discrete time level) is an example of a semi-implicit approximation to df/dt = g(f) + h(f). Semi-implicit approximations may increase computational efficiency when g produces relatively higher frequencies or more rapid time changes in f than does h.
See implicit time difference.