Example 4.  Solve Laplace's equation over the square [Graphics:Images/EllipticPDEMod_gr_70.gif] where the boundary conditions are  
    Top:       180  
    Left:         80  
    Bottom:   20  
    Right :        0  

Solution 4.

Suppose that the orientation refers to the "standard" the x-y plane. After we graph the solution we can "modify" the labels in the tick marks to suit our fancy.

 

[Graphics:../Images/EllipticPDEMod_gr_71.gif]

Next, solve it.

[Graphics:../Images/EllipticPDEMod_gr_72.gif]

[Graphics:../Images/EllipticPDEMod_gr_73.gif]
[Graphics:../Images/EllipticPDEMod_gr_74.gif]

Plot the solution. Change the axes labels to "x" and "y" and manually supply the tick marks that correspond to these labels.

[Graphics:../Images/EllipticPDEMod_gr_75.gif]


[Graphics:../Images/EllipticPDEMod_gr_76.gif]

[Graphics:../Images/EllipticPDEMod_gr_77.gif]

[Graphics:../Images/EllipticPDEMod_gr_78.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004