Similar expressions can be written for the second derivative with respect to the y and z coordinates.
In the finite difference method, the computational domain is discretized using a 3D rectangular grid as shown on the figure below. The grid spacing along the three principal coordinate axes is denoted by Δx, Δy and Δz, respectively. In this grid, the coordinates of any point (x,y,z) in the space can be expressed as x = iΔx, y = jΔy and z = kΔz. Therefore, every point can simply be represented by an index triplet (i,j,k).
<table>
</table>
The potential at any the point (x,y,z) in the space can be expressed in terms of the potentials at its six neighboring grid points along the principal axes. The This creates a 7-point computational molecule shown in the figure below:
<table>