Example 7. Use Picard
iteration to find and plot approximations for the solution
of the I.V.P.
Solution 7.
![[Graphics:../Images/PicardIterationMod_gr_137.gif]](../Images/PicardIterationMod_gr_137.gif)
Picard iteration for generating the first six approximations is started with the Mathematica command:
![[Graphics:../Images/PicardIterationMod_gr_139.gif]](../Images/PicardIterationMod_gr_139.gif)
![[Graphics:../Images/PicardIterationMod_gr_140.gif]](../Images/PicardIterationMod_gr_140.gif)
![[Graphics:../Images/PicardIterationMod_gr_141.gif]](../Images/PicardIterationMod_gr_141.gif)
Now we can graph the Picard approximations.
![[Graphics:../Images/PicardIterationMod_gr_143.gif]](../Images/PicardIterationMod_gr_143.gif)
![[Graphics:../Images/PicardIterationMod_gr_144.gif]](../Images/PicardIterationMod_gr_144.gif)
![[Graphics:../Images/PicardIterationMod_gr_146.gif]](../Images/PicardIterationMod_gr_146.gif)
![[Graphics:../Images/PicardIterationMod_gr_147.gif]](../Images/PicardIterationMod_gr_147.gif)
![[Graphics:../Images/PicardIterationMod_gr_149.gif]](../Images/PicardIterationMod_gr_149.gif)
![[Graphics:../Images/PicardIterationMod_gr_150.gif]](../Images/PicardIterationMod_gr_150.gif)
(c) John H. Mathews 2005