# Finite-difference equation

From AMS Glossary

## finite-difference equation

An equation resulting from the use of finite-difference approximations to the derivatives in an ordinary or partial differential equation.

A finite-difference equation may have a solution (or solutions) the behavior of which is quite unlike that (or those) of the differential equation approximated, and care must be taken to exclude or minimize any such solutions in the computation. Finite-difference equations are extensively used in meteorology, a realistic atmosphere usually being described by equations without tabulated solutions.

*See*computational mode.