Example 3.  Use Picard iteration to find and plot approximations for the  solution of the I.V.P.  

        [Graphics:Images/PicardIterationMod_gr_48.gif].  

Solution 3.

[Graphics:../Images/PicardIterationMod_gr_49.gif]

[Graphics:../Images/PicardIterationMod_gr_50.gif]

Picard iteration for generating the first six approximations is started with the Mathematica command:

[Graphics:../Images/PicardIterationMod_gr_51.gif]

[Graphics:../Images/PicardIterationMod_gr_52.gif]

 

We can graph the analytic solution and the Picard iterations.

[Graphics:../Images/PicardIterationMod_gr_53.gif]


[Graphics:../Images/PicardIterationMod_gr_54.gif]

[Graphics:../Images/PicardIterationMod_gr_55.gif]

 

 

 

[Graphics:../Images/PicardIterationMod_gr_56.gif]


[Graphics:../Images/PicardIterationMod_gr_57.gif]

[Graphics:../Images/PicardIterationMod_gr_58.gif]

 

 

 

[Graphics:../Images/PicardIterationMod_gr_59.gif]


[Graphics:../Images/PicardIterationMod_gr_60.gif]

[Graphics:../Images/PicardIterationMod_gr_61.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005