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1.3.4 Second derivatives in 2 dimensions
By again fixing one of the independent variables
 , say  and considering only , we obtain, in terms of the
Stirling (centered) approximation,
Analogous (and less accurate) formulae are valid within the
NGF and NGBapproximations, respectively.
How about
mixed derivatives?
Mixed derivatives
Approximating use the same
kind of approximation with respect to both the  and the direction.
(This may not hold if and have a different character, e.g. one
space and one time variable.)
Stirling:
And now, fow for the
curvature of :
Curvature of a function f(x,y)
To find the local curvature at the grid point
we have to apply the nabla operator twice.(*)
There are two ways:
Either ``difference'' along the grid axes,
or apply ``diagonal differencing'', writing
 


Axial vs. diagonal differencing

(*) Note that the nabla operator mentioned here is not
to be mixed up with the backward difference for which we
use the same symbol.
Next: 1.4 Sample Applications
Up: 1.3 Difference Quotients
Previous: 1.3.3 First derivatives in
Franz J. Vesely Oct 2005
See also: "Computational Physics  An Introduction," KluwerPlenum 2001