Example 4.  Reduce the step size by   and see what happens to the error.
Recalculate points for Runge-Kutta's method, and the analytic solution using twice as many subintervals.
Then Plot the error for Runge-Kutta's method.

Solution 4.

The error for Runge-Kutta's method.

Compare the error for Runge-Kutta's method with 25 and 50 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