Definition:Finite Difference Operator/Central Difference

Definition

Let $f: \R \to \R$ be a real function.

Let $h \in \R_{>0}$.

The central difference operator on $f$ is defined as:

$\map {\delta_h f} x := \map f {x + \dfrac h 2} - \map f {x - \dfrac h 2}$

Also see

• Definition:Forward Difference Operator
• Definition:Backward Difference Operator

• Results about the central difference operator can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): finite differences
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): central difference
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): finite differences