I have the following function:
$$\frac{1024\,x^4}{e^{(4x)^{4}}}$$
And I applied the composed Simpson rule to obtain the value of the integral of that function from $0$ to $0,62715.$ Then, I applied the Romberg Method to obtain a better approximation for the same number of sub-intervals. But when I have done that, I discovered that the Romberg method, for the same number of subdivisions made my approximation worse.
The formula that I've used for each extrapolation of the Romberg Method was:
$$R(k,m) = \frac{4^m\cdot R(k+1,m-1)-R(k,m-1)}{4^m-1} $$
Is it even possible that the Romberg method makes the aproximation worse?
