There is a following task for a friend of mine to make:
$$-\Delta u=f,x\in(0,X),y\in(0,Y)\\-u_x+\alpha(y)u\Bigr|_{x=0}=g(y)\\u\Bigr|_{x=X}=c(y)\\u\Bigr|_{y=0}=a(x)\\u\Bigr|_{y=Y}=b(x)$$
She needs to make a program using biconjugate gradient method to solve the problem.She managed to implement the method but I don't know what matrix should she use and how does she need to enter it in Matlab.
I would appreciate you if you helped me with the matrix
The system of equations will be the same as the one discussed in the Wikipedia article "Discrete Poisson equation". To enter it into Matlab, I would suggest looking into the `spdiags` command. (This function uses the "sparse matrix" format, which will significantly speed up calculations involving large matrices/fine discretizations.)