Definition:Finite Difference Operator/Forward Difference

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


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

$\map {\Delta_h f} x := \map f {x + h} - \map f x$


Also see

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


Sources