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 .