I am trying to model a packed bed distillation column for a binary liquid in Python. Unfortunately, when I set up my system, I end up with a system of coupled non-linear first order ODEs with boundary conditions at opposite ends (feed conditions and exit conditions), and I do not know how to solve this sort of problem. I know how to solve coupled non-linear ODEs with boundary conditions at the same end, and SciPy has a coupled ODE solver in any case, but I do not know any strategies for solving coupled ODEs with boundary conditions at different ends. Can anyone recommend a source for reading up on strategies? Or know of any libraries with such solvers (esp. in Python)? This is mostly for entertainment, so if this is an ultra difficult problem, I am willing to give up.