Example 2.  Consider the D. E.  [Graphics:Images/ShootingMod_gr_70.gif]  over  [Graphics:Images/ShootingMod_gr_71.gif]  with  [Graphics:Images/ShootingMod_gr_72.gif]  and  [Graphics:Images/ShootingMod_gr_73.gif].
Use the "linear shooting" method and solve for the first function u(t).  

Solution 2.

Enter the function  p(t), q(t) and r(t) into Mathematica.  

[Graphics:../Images/ShootingMod_gr_74.gif]



[Graphics:../Images/ShootingMod_gr_75.gif]

[Graphics:../Images/ShootingMod_gr_76.gif]

[Graphics:../Images/ShootingMod_gr_77.gif]

[Graphics:../Images/ShootingMod_gr_78.gif]

[Graphics:../Images/ShootingMod_gr_79.gif]


The method involves solving a two systems of equations over  [Graphics:../Images/ShootingMod_gr_80.gif],  

First solve     
    [Graphics:../Images/ShootingMod_gr_81.gif]                        with    [Graphics:../Images/ShootingMod_gr_82.gif],  
    [Graphics:../Images/ShootingMod_gr_83.gif]    and    [Graphics:../Images/ShootingMod_gr_84.gif].  
For the latter equation use the function

[Graphics:../Images/ShootingMod_gr_85.gif]


[Graphics:../Images/ShootingMod_gr_86.gif]

[Graphics:../Images/ShootingMod_gr_87.gif]

Send this to the Runge2D subroutine.

[Graphics:../Images/ShootingMod_gr_88.gif]

The first solution we obtain is u.

 

[Graphics:../Images/ShootingMod_gr_89.gif]

Now we can plot the solution.

[Graphics:../Images/ShootingMod_gr_90.gif]


[Graphics:../Images/ShootingMod_gr_91.gif]

[Graphics:../Images/ShootingMod_gr_92.gif]

[Graphics:../Images/ShootingMod_gr_93.gif]
[Graphics:../Images/ShootingMod_gr_94.gif]

[Graphics:../Images/ShootingMod_gr_95.gif]
[Graphics:../Images/ShootingMod_gr_96.gif]

[Graphics:../Images/ShootingMod_gr_97.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004