Perhaps the most traditional way to solve (1) utilizes the finite
difference approach by discretizing the solution domain 
using a
grid of quadralaterals (for 2D) or cubes (for 3D). The coordinates of a
typical grid point are 
, and the value
of 
at a grid point is denoted by 
. Taylor's
theorem can then be utilized to provide the difference equations (see the
section on Some High Performance Computing Issues in
Partial Differential
Equations
).
For example:
with similar equations for
.
