Hi, I am trying to solve the Poisson type equation for the pressure on the form:

del2(P)-C(x,y)*grad(P)=f(x,y)

If I wanna descretize this equation, should I deal with the higher derivative terms only and consider the lower derivative terms as a source term? I mean (for 1-D case):

d2P/dx2 = C(x)*(dP/dx)+f(x)

Any specific method to solve this type of equation?

Since this is a linear equation, I'd be tempted to descretize the entire equation (first and second derivatives), then solve it using Gaussian elimination. You'll get a banded coefficient matrix (unless you have periodic boundary conditions which can complicate things a bit), which is pretty efficiently stored and solved. There may be a conditioning problem for the matrix if C is too large.

Good luck!