Definition:Central Difference Operator/Mistake

Source Work

2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.):

central difference

Mistake

Given *function values $y_i = \map f {x_i}$, where $x_i = x_0 + i h$, $i = 0, 1, 2, \ldots,$ the central difference $\delta_{i + 1/2}$ is defined by $\delta_{i + 1/2} = y_{i + 1} - y_i$.

Correction

This is incorrect, as it is the same definition as for the (first) forward difference operator.

The correct formula is:

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

The astute reader will immediately notice that, as defined, it is not certain that the function values for $x_i \pm \dfrac 1 2$ are not necessarily available, or even defined.

Also see

The same mistake is made in the entry finite differences.

Sources

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