# Implicit time difference

From AMS Glossary

## 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 Δ*t*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*(*f*^{n}) or*g*(*f*^{n - 1}). Implicit time differences are relatively more stable and allow larger time steps than explicit time differences.*Compare*leapfrog differencing.