Integrating ODE system over gridded data

[ChrisRackauckas]

@archermarx

My first attempt involved constructing cubic interpolations using Interpolations.jl through the data to transform each →Y––\vec{\underline{Y}} into Y––(x)\underline{Y}(x) , so that all of my known data variables become functions of position only. However, the system is blowing up and still seems fairly unstable (only advances a few iterations). I think there may be errors in my setup causing this, but as I address those, I wanted to make sure that this approach is a good one, and if not, what might I do instead?

That is generally the approach one would use on this kind of problem.