Example 3. Use
Picard iteration to find and plot approximations for
the solution of the I.V.P.
.
Solution 3.
Picard iteration for generating the first six approximations is started with the Mathematica command:
![[Graphics:../Images/PicardIterationMod_gr_52.gif]](../Images/PicardIterationMod_gr_52.gif)
We can graph the analytic solution and the Picard iterations.
![[Graphics:../Images/PicardIterationMod_gr_54.gif]](../Images/PicardIterationMod_gr_54.gif)
![[Graphics:../Images/PicardIterationMod_gr_55.gif]](../Images/PicardIterationMod_gr_55.gif)
![[Graphics:../Images/PicardIterationMod_gr_57.gif]](../Images/PicardIterationMod_gr_57.gif)
![[Graphics:../Images/PicardIterationMod_gr_58.gif]](../Images/PicardIterationMod_gr_58.gif)
![[Graphics:../Images/PicardIterationMod_gr_60.gif]](../Images/PicardIterationMod_gr_60.gif)
![[Graphics:../Images/PicardIterationMod_gr_61.gif]](../Images/PicardIterationMod_gr_61.gif)
(c) John H. Mathews 2005