Successive over-relaxation method - SOR

From CFD-Wiki

We seek the solution to set of linear equations:

For the given matrix A and vectors X and Q.
In matrix terms, the definition of the SOR method can be expressed as :

Where D,L and U represent the diagonal, lower triangular and upper triangular matrices of coefficient matrix A and k is iteration counter.
is extrapolation factor.

The pseudocode for the SOR algorithm:

Algorithm

Chose an intital guess to the solution

for k := 1 step 1 untill convergence do

for i := 1 step until n do

for j := 1 step until i-1 do

end (j-loop)

for j := i+1 step until n do

end (j-loop)

end (i-loop)

check if convergence is reached

end (k-loop)