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Let be given for equidistant values of and , respectively:
We will use the short notation
etc. for the partial derivatives of the function with
respect to its arguments.
Note: One of the arguments may be the time : etc.
For the numerical treatment of partial differential
equations (PDEs) we again have to construct discrete
approximations to the partial derivatives at the base points
.
Using the
DNGF, DNGB, or DST approximation of lowest order, we have
or
or
Again, the central difference scheme is superior.
But what about
second derivatives?
Next: 1.3.4 Second derivatives in
Up: 1.3 Difference Quotients
Previous: 1.3.2 Second Derivatives
Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001