Example 3.  Use the "linear shooting" method and solve for the second function v(t).  

Solution 3.

Next, solve  
    [Graphics:../Images/ShootingMod_gr_98.gif]                        with    [Graphics:../Images/ShootingMod_gr_99.gif],   
    [Graphics:../Images/ShootingMod_gr_100.gif]    and    [Graphics:../Images/ShootingMod_gr_101.gif].  
For the latter equation use the function

[Graphics:../Images/ShootingMod_gr_102.gif]


[Graphics:../Images/ShootingMod_gr_103.gif]

[Graphics:../Images/ShootingMod_gr_104.gif]

Send this to the Runge2D subroutine.

 

[Graphics:../Images/ShootingMod_gr_105.gif]

The second solution we obtain is v.

 

[Graphics:../Images/ShootingMod_gr_106.gif]

Now we can plot the solution.

[Graphics:../Images/ShootingMod_gr_107.gif]


[Graphics:../Images/ShootingMod_gr_108.gif]

[Graphics:../Images/ShootingMod_gr_109.gif]

[Graphics:../Images/ShootingMod_gr_110.gif]
[Graphics:../Images/ShootingMod_gr_111.gif]

[Graphics:../Images/ShootingMod_gr_112.gif]
[Graphics:../Images/ShootingMod_gr_113.gif]

[Graphics:../Images/ShootingMod_gr_114.gif]

Notice we are in luck, since  [Graphics:../Images/ShootingMod_gr_115.gif].  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004