Solution 2.

Remark.  We will be using  [Graphics:../Images/FiniteDifferencePDEMod_gr_55.gif] .  This forces  [Graphics:../Images/FiniteDifferencePDEMod_gr_56.gif].

Remark.  Clear the old "rule" for F, otherwise it will be hanging around.  The piecewise definition of the function [Graphics:../Images/FiniteDifferencePDEMod_gr_57.gif] can be accomplished as follows.

[Graphics:../Images/FiniteDifferencePDEMod_gr_58.gif]


[Graphics:../Images/FiniteDifferencePDEMod_gr_59.gif]

 

 

 

[Graphics:../Images/FiniteDifferencePDEMod_gr_60.gif]


Now set up the table of solutions.  Solve it.  Plot it.  

[Graphics:../Images/FiniteDifferencePDEMod_gr_61.gif]


[Graphics:../Images/FiniteDifferencePDEMod_gr_62.gif]

[Graphics:../Images/FiniteDifferencePDEMod_gr_63.gif]

[Graphics:../Images/FiniteDifferencePDEMod_gr_64.gif]

[Graphics:../Images/FiniteDifferencePDEMod_gr_65.gif]

[Graphics:../Images/FiniteDifferencePDEMod_gr_66.gif]

[Graphics:../Images/FiniteDifferencePDEMod_gr_67.gif]

[Graphics:../Images/FiniteDifferencePDEMod_gr_68.gif]

[Graphics:../Images/FiniteDifferencePDEMod_gr_69.gif]
[Graphics:../Images/FiniteDifferencePDEMod_gr_70.gif]
[Graphics:../Images/FiniteDifferencePDEMod_gr_71.gif]
[Graphics:../Images/FiniteDifferencePDEMod_gr_72.gif]
[Graphics:../Images/FiniteDifferencePDEMod_gr_73.gif]


To see the numerical values enter the command:

[Graphics:../Images/FiniteDifferencePDEMod_gr_74.gif]



[Graphics:../Images/FiniteDifferencePDEMod_gr_75.gif]

[Graphics:../Images/FiniteDifferencePDEMod_gr_76.gif]

[Graphics:../Images/FiniteDifferencePDEMod_gr_77.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004