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# Numerical Methods-Simpson's Rule MEI NM Tweet

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1. Numerical Methods-Simpson's Rule MEI NM
Hi,

I'm having trouble with question 2 in the paper above. I can calculate the trapezium and midpoint rule estimates with h=0.5 fine, but I don't understand how to calculate the Simpson's rule estimate with h=0.25 without calculating more trapezium and midpoint rule values.

The markscheme (http://www.ocr.org.uk/download/ms_07..._l_gce_jun.pdf) says to use the formula Sn=2Mn+Tn/3, and this works, but I don't see why it does without more values.

Can anyone help?
2. Re: Numerical Methods-Simpson's Rule MEI NM
Anyone?
3. Re: Numerical Methods-Simpson's Rule MEI NM
4. Re: Numerical Methods-Simpson's Rule MEI NM
You don't (really) use a step value (of h) when using Simpson's rule. You use a mid-point value.

Simpson's rule is

When the question says, use , that's because the interval is 0.5, giving a mid-point value of 0.25.

When it says use a step value of that means split the interval up into two intervals, each of length and mid-point values of

Now use Simpson's rule to work out the areas of the two sub-intervals and then add them together.
5. Re: Numerical Methods-Simpson's Rule MEI NM
(Original post by steve10)
You don't (really) use a step value (of h) when using Simpson's rule. You use a mid-point value.

Simpson's rule is

When the question says, use , that's because the interval is 0.5, giving a mid-point value of 0.25.

When it says use a step value of that means split the interval up into two intervals, each of length and mid-point values of

Now use Simpson's rule to work out the areas of the two sub-intervals and then add them together.
Thanks