# Poisson-type equation

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 February 7, 2002, 10:13 Poisson-type equation #1 Ammar Guest   Posts: n/a 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?

 February 7, 2002, 14:02 Re: Poisson-type equation #2 Jim Park Guest   Posts: n/a 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!

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