What is the order of the midpoint rule?
By Emma Payne •
If the Trapezoidal-Rule has the order $n=1$, and Simpson's has order $n=2$, what is the order $n$ of the midpoint rule?
And if the weights of the Trapeziumrule are ($1/2, 1/2$) and those of the Simpson-Rule are ($1/6, 4/6, 1/6$), what are the weights of the midpoint-rule?
Thank you in advance!
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$\begingroup$The error of the Midpoint rule is
$Error_m \leq \frac{k(b-a)^3}{24n^2 } = k(b-a)h^2/24$. So it equals to $O(h^2)$, where $k = max|f"|$.
$\endgroup$ 1 $\begingroup$The order of the midpoint rule is $n=2$. For examples, you can see Why does Trapezoidal Rule have potential error greater than Midpoint?
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