It is precisely on sophisticated numerical libraries that i found
octave severely lacking. For example for solving differential
equations with boundary values, scilab has colnew (bvode), matlab has
something equivalent, but at the time octave had nothing (maxima also
has colnew nowadays). Maybe the situation has changed, but when i
looked octave had only the most elementary stuff (it was many years
ago). For the most interesting stuff (e.g. numerically solving PDEs)
i think only matlab is adequate, or even has something.