Problem with DifferentialEquations.jl

[magic dagger]

I'm working on a project, which is basically a simulation model for adsorption process of phosphate in waste water

(2 videos to understand the adsorption process, it's 15 seconds in total)

https://www.youtube.com/watch?time_continue=15&v=XnkKa9xlw-c&embeds_referring_euri=https%3A%2F%2Fencyclopedia.che.engin.umich.edu%2F&source_ve_path=MjM4NTE
https://www.youtube.com/watch?v=xQDV57ZthC8&t=9s

So the first is to simulate the evolution of the concentration of phosphate into the column and the evolution of the amount of phosphate adsorbed into the column. To do that, I have to discretize two equations.

I'm using a code that I've previously used in class with slighty different equations, and it was working perfectly. However in my case, I keep getting weird plot with excessive time or maxiters error.

The last file is to calculate the concentration at the equilibrium from lab data. All you need to know is that the vector q need to have the same amount of element than the number of space points.

Exemple of what I get

What I should get

[fallen rapids]

Can’t check your code at the moment, but the central difference seems to lack 1/2
(It wouldn’t matter, as it can be considered to be effectively part of the coefficient before)

You might want to use upwind scheme for stability (because it seems your solution isn’t stable)

… I’m sure someone who’s more familiar with differential equation.jl can provide a better solution

[formal grove]

yes that is not a stable semidiscretization