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I was just wondering if I could have some assistance in regards to the Trapezoidal Rule and Simpson's Rule.

I have a question where it asks to generalize the Trapezoidal Rule to the case of Simpson's Rule - which the aim is to compute further approximations without having to recalculate any f's. Apparently we have to start with Richardson extrapolation to show how it can be derived.

Trapezoidal Rule: I[2n] (a,b)=1/2 I[n] (a,b)+(b-a)/2N f(x[2j+1])

Many thanks, !

orangesun
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  • Does this posting help? http://math.stackexchange.com/questions/113667/relation-between-simpsons-rule-trapezoid-rule-and-midpoint-rule?rq=1 – Amzoti May 05 '13 at 21:03
  • Thank you, it does help heaps - I am still wondering though how to derive Simpson's Rule from Trapezoidal Rule using richardson extrapolation – orangesun May 06 '13 at 05:49

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