Simpsons Rule - Unequal Stations

Hi all - I am trying to use the simpsons rule but hit a road block with uneven spacing between stations/points. I have worked with half stations before, but this one has me stumped...

Say I have 9 stations, each 1.0m apart - therefore a half station is 0.5m.
8 (SM: 1)
7 (SM: 4)
6 (SM: 2)
5 (SM: 4)
4 (SM: 2)
3 (SM: ?)
2.5 (SM: ?)
2 (SM: ?)
1(SM: ?)
0.5 (SM: ?)
0(SM: ?)

I am not sure what the Simpson multipliers are because I am not sure what to do between stations 0.5 and 2.5

Just to show - I can work out the Simpons multipliers for the following unequal spacing...
8 (SM: 1)
7 (SM: 4)
6 (SM: 2)
5 (SM: 4)
4 (SM: 2)
3 (SM: 4)
2 (SM: 1.5)
1.5 (SM: 2)
1 (SM: 1)
0.5 (SM: 2)
0 (SM: 0.5)

Am I missing something very obvious?

 

I'm not sure if I understood your point.
If it is a practical problem:
This link leads to a VBA Excel folder with a spline function generator. Using this folder, you will be able to put in your data (stations and corresponding values) and as a result you can pick the values of equidistant spacings.
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Simpson's rule works for an even number of equally spaced stations. It won't work with 9 stations, you need to use a different method.
Simpson's Rule -- from Wolfram MathWorld http://mathworld.wolfram.com/SimpsonsRule.html
Mathwords: Simpson's Rule http://www.mathwords.com/s/simpsons_rule.htm

 

With the folder mentioned above, you are also able to choose a different number of stations.
E. g.:
Given a sheerline with 9 unequal stations (values in mm, x = locus of station; y = height of sheerline from base plane):


The graph shows the spline and the station points in it (red):


The output sheet shows the respective numerical values:


You choose 10 Stations, which means 9 intervals. Divide the 5486 by 9 and add the result once, twice and so on in the 'living' area:


The results for 10 stations are given in the column y.
So you are no longer depending on the original stations and their values and it should be easy to apply Simpson's rule to the new data.

 

However, if you are using software it probably doesn't make sense to solve by hand using Simpson's rule. Might as well use integrating software.

 

Regarding your first list of stations, is there a smooth transition between 0 and 1 also 2 and 3. If so are you gaining anything by using the .5 and 2.5 stations, much easier to ignore them.
If you finished up with an uneven number of stations e.g. 9, you could use Simpson's rule for the first 8 stations then add ( station 8 + station 9 ) /2 times the spacing. Choose the end that has the least change between stations to minimise the error.