@acer I am working with a computational fluid dynamics solver which is currently a 2 dimensional solver (in Fortran). My goal is to expand this solver to three dimensions. The 2D solver was written in such a way that the computation talked about in this thread was done analytically. To avoid scrapping this entire portion of the code (and avoid changing other subroutines), I was hoping to do an analytic computation in 3D such that it could easily be implemented in Fortran. As we have seen, analytical solutions to this problem are too complex, and I will more than likely need to rely on numerical computations. I have some ideas on how this solution could possibly be obtained analytically (possibly with some clever substitution or rewriting my independed variables in non-conservative form). More than likely, this will fail and I will need to rewrite a large portion of the code in order to implement something such as LAPACK. I will continue to try more analytical methods first, however. Thank you very much for your help over the past couple of days as I am not used to using MAPLE, your help is very appreciated.