Definition:Finite Difference Operator/Central Difference

Definition

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

Let $y = \map f x$ have known values:

$y_k = \map f {x_k}$

for $x_k \in \set {x_0, x_1, \ldots, x_n}$ defined as:

$x_k = x_0 + k h$

for some $h \in \R_{>0}$.

First Central Difference Operator

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

$\delta_{i + 1/2} := \map f {x_i + \dfrac h 2} - \map f {x_i - \dfrac h 2}$

for $i = 1, 2, \ldots, n - 1$

Also see

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

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

Sources

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

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