# Semi-implicit method

From AMS Glossary

## semi-implicit method

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

The approximation (

*f*^{n + 1}-*f*^{n - 1})/2Δ*t*=*g*(*f*^{n + 1}) +*h*(*f*^{n}) (where superscript*n*denotes a point in time, separated by step Δ*t*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.