I just wanted to ask a quick question in regards to simpson's rule for integration. I have been reading up on the trapezoidal rule, and have found the notations and have an understanding such that:
Where, $T(n) =$ trapezoidal rule formula
and have gathered that $$ T(2n) = {1\over 2} T(n) + \text{sum of the odd terms} $$
From this, is it right to say $T(n)$ is a more accurate calculation than $T(2n)$, right?
Another question I have is that I have a question in which I have to calculate $S(2n)$ using richardson extrapolation which i have the formula:
$$ S(2n) = {4\over 3} T(2n) - {1\over 3} T(n) $$ From this, is it right to conclude that $S(n)$ is more accurate than $S(2n)$?
....I have a few more questions to follow up on, but for now I just wanted to check my understanding
If that is all correct, I was wondering how do we actually start calculating $S(2n)$ and how to find $S(4n)$ and to express $S(4n)$ in terms of $S(2n)$ without $T(2n)$ or $T(n)$ in the formula