Example 7. Use Picard iteration to find and plot approximations for the  solution of the I.V.P.  

        [Graphics:Images/PicardIterationMod_gr_135.gif]    

Solution 7.

[Graphics:../Images/PicardIterationMod_gr_136.gif]

[Graphics:../Images/PicardIterationMod_gr_137.gif]

 

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

[Graphics:../Images/PicardIterationMod_gr_138.gif]

[Graphics:../Images/PicardIterationMod_gr_139.gif]

[Graphics:../Images/PicardIterationMod_gr_140.gif]

[Graphics:../Images/PicardIterationMod_gr_141.gif]

 

Now we can graph the Picard approximations.

[Graphics:../Images/PicardIterationMod_gr_142.gif]


[Graphics:../Images/PicardIterationMod_gr_143.gif]

[Graphics:../Images/PicardIterationMod_gr_144.gif]

 

 

 

[Graphics:../Images/PicardIterationMod_gr_145.gif]


[Graphics:../Images/PicardIterationMod_gr_146.gif]

[Graphics:../Images/PicardIterationMod_gr_147.gif]

 

 

 

[Graphics:../Images/PicardIterationMod_gr_148.gif]


[Graphics:../Images/PicardIterationMod_gr_149.gif]

[Graphics:../Images/PicardIterationMod_gr_150.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005