Sorry about the format, bit I have no knowledge of LateX. A,B - are real constants U=(Ux,Uy,Uz) I have a system of three coupled linear second order differential equations (di)^2(Ui) +A*Laplacian(Ui)+ B*di[Divergence(U)] Note: The first term is not a sum. 0<z<H, while x & y can be any real number. I have some more boundary conditions, but I feel as if I'm nowhere close to that stage. I'm pretty stumped. I tried Fourier transforming (in x & y) and end up with a system of six coupled linear ODEs. I can find the eigenvalues (they're the roots of a cubic equation), but solving for the eigenvectors is an awful algebraic exercise. Is there anything I'm missing?