Example 1.  Solve Laplace's equation over a  9 by 9  grid with boundary conditions
    Top:       180
    Left:         80
    Bottom:   20
    Right:        0

Solution 1.

Remark.  The traditional way to teach the solution of elliptic PDE's is the following way, which just deals with the matrix elements and if needed the graphics is "old style" and just deals with plotting the grid.  Usually there is no labeling of the axes.  In example 3 we will see that a much more complicated data structure and graphics capabilities are needed to make thing better.  

Next, solve it.

Plot the solution.

To see the numerical values enter the command:

We can make a contour plot of the solution.  However, to get the orientation like the table and the 3D figure requires reversing the rows in the matrix.

It is remarkable that we can obtain a contour plot from a set of data points.  As usual for list plots, the axes represent the number of the row and column and not the interval that were given.  

(c) John H. Mathews 2004