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

Solution  4.

The error for Taylor series 's method.

Compare the error for Taylor  series '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