Example 8.  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  8.

The error for Taylor  series 's method.

Compare the error for Taylor series '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