Using interval halving determine the order of the method?

Question

(b) When a particular numerical method involving interval halving is used to evaluate the integral,

,

b

I = [ f (x) dx

a

the following table is generated:

Number of Strips -- Approximate value of I

1 -- 3.5

2 -- 2.212

4 -- 2.0275

8 -- 2.00344

16 -- 2.00043

Given that the true value of the integral is I =2 , determine the order of the method.

Answer 1

Wikipedia "Numerical Methods" reminds me that:

The local error of the method is the error committed by one step of the method. That is, it is the difference between the result given by the method, assuming that no error was made in earlier steps, and the exact solution:

The method has order p if

  error = O(step-size^{p+1})  as step-size -> 0

Here the error at step-size 1/16 is 0.00043

so it seems the order is almost 2  (because (1/16)^3 = .0004 approx

I hope this is correct!