# Finite-difference approximation

From AMS Glossary

## finite-difference approximation

The difference between the values of a function at two discrete points, used to approximate the derivative of the function.

The derivative where Δ where δ where ∇

*f*′(*x*) of a function*f*(*x*) at an arbitrary point*x*is usually approximated by finite differences in one of three ways:*f*is called a forward difference;*f*is called a centered difference;*f*is called a backward difference (not to be confused with the gradient). Of these approximations, the centered difference is the most accurate; whether it is the most convenient or accurate for the problem as a whole depends on the character of the equations involved. Higher derivatives are approximated by iteration of these formulas.