Example 8.  Reduce the step size by   and see what happens to the error.
Recalculate points for Milne-Simpson's method, and the analytic solution using twice as many subintervals.
Then Plot the error for Milne-Simpson's method.

Solution 8.

The error for Milne-Simpson's method.

and the step size h = 0.05

Compare the error for Milne-Simpson's method with 50 and 100 subintervals.
Question 1. When the step size is reduced by estimate how much is the error reduced ?  (Theoretically is is .)  

(c) John H. Mathews 2004