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Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods
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1 Reddit comment about Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods:

u/metleb ยท 1 pointr/matlab

Are T_gas and P functions of time or just z?

If they're only functions of z and don't change with time--assuming you're trying to solve for C_i--this is a relatively straightforward PDE to solve, of the form dC_dt = a*dC_dz + b*C + d. You can use a finite difference method, like Euler's Forward / Explicit, to discretize both space and time. You then stick it in a loop to march through each time step until you reach steady-state or you get bored.

If you're using Euler's forward method, each time step would look something like:

C_next = C_now + dt * (a * gradient(C_now, dz) + b * C_now + d)

This is my favourite book on PDEs: https://www.amazon.ca/Numerical-Methods-Partial-Differential-Equations/dp/0128498943 but it's probably at the library!