Example 12.  Use Picard iteration to find and plot approximations for solution of the second order I.V.P.  

        .  

Solution 12.

First define the function  , and   and the initial conditions        by typing:

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

We can graph the analytic solution and the Picard iterations.

(c) John H. Mathews 2005