Example 8. Use Picard iteration to find and plot approximations for the  solution of the I.V.P.  

            

Solution 8.

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

We are done!

Aside.  Mathematica can find the analytic solution.

We can plot the analytic solution.  

We can plot the analytic solution and the first three Picard approximations.

We can plot the analytic solution and the second three Picard approximations.

We can plot the analytic solution and the first six Picard approximations.

(c) John H. Mathews 2005