# 2D Milne's rule composite integration

1. Oct 27, 2014

### presto

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. Oct 27, 2014

### presto

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
3. Nov 2, 2014

### Staff: Mentor

The OP has been banned, so closing this thread.