sir,

I don't understand the SIP (http://en.wikipedia.org/wiki/Stone_method). what does N represent

Ax = (M-N)x = (LU-N)x = b

in the above equation A and b are known values , what is the need of iteration here.

A is known but finding Ainv is very difficult, so we prefer iterating. (to know x you need to know Ainv).

could you explain breif about this algorithm.

on cfd-online, in the wiki there is a section on numerical methods, there you will find the link about stone's method. Read that.

A contains 5 diagonals (Poisson equation discretisation result via the 5 points scheme).

If we try to performe the incomplete LU decomposition, L and U will contain 3 diagonals each, but the multiplication will produce M with 7 diagonals, so N must contain at minimum 2 diagonals of M that correspond to zero diagonals of A.

So M = L*U and M-N = A

yes i got 7 diagonals. with L has 3 diagonals, U 2 diagonals the additional two diagonals are stored in N matrix. Could you please expalin how to proceed after this. all are sparse matrix, so how to solve this equation.

The best advice I can give you is to look for this book "Computational methods for Fluid Dynamics", Ferziger & Peric, the SIP is clearly explained and you also can download book codes.

Email me if you have difficulties to find them.

sir, how to download codes from peric book... could you please give your mail id

this is mail id d_santhosh2@yahoo.com