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2D Milne's rule composite integration

  1. Oct 27, 2014 #1
    http://en.wikipedia.org/wiki/Newton–Cotes_formulas

    Simpson rule: 1 4 1, and the composite version: 1 4 2 4 2 4 2 4 ....4 1
    in a double integral we just compute rows, and next columns, a this gives a matrix:
    http://mathfaculty.fullerton.edu/mathews/n2003/SimpsonsRule2DMod.html

    Milne's rule is: 2 -1 2, thus a composite version should be probably:
    2 -1 4 -1 4 -1 ... -1 2


    for 2D we have 2n+1 such rows, then I must apply the same rule to the rows,
    but I don't konow how do that...

    in a first column there are 2 only, in a second -1, ext.

    then I apply the 2 -1 2 scheme to these 2s, but how: adding or multipling by these numbers: 2 -1 2 ?
     
  2. jcsd
  3. Oct 27, 2014 #2
    4 -2 8 -2 8 -2 8 -2 4
    -2 1 -4 1 -4 1 ...
    8 -4 16 -4 16 -4
    -2 1 -4 1 -4 1
    8 -4 16 -4 16 -4
    -2 1 -4 1 -4 1
    4 -2 8 -2 8 -2

    probably something like this... and a single rule in 2D:

    4 -2 4
    -2 1 -2
    4 -2 4

    4*4 - 4*2 + 1 = 9
     
    Last edited: Oct 27, 2014
  4. Nov 2, 2014 #3

    Mark44

    Staff: Mentor

    The OP has been banned, so closing this thread.
     
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