How to solve convection diffussion equation

Hello,

I want to solve the following equation in Matlab, but I have no idea how to do it:

u*dC/dz = Dh*d^2C/dx^2+Dv*d^2C/dz^2

Kind regards, Teun

[Youssef Khmou]

is the first component correct? i think it should be dC/dt

[Teun]

No I am looking at steady state. dC/dz is the convection term, d^2C/dx^2 is the lateral dispersion term and d^2C/dz^2 is the axial dispersion term.

Answer 1

[Teun]

Thank you Shoaibur, I understand the discritezition but can you be a little more specific about how to solve this in Matlab.

I can set up a matrix with the coefficients: [u/dz, Dh/dx^2,....]=[0] and solve this to get a Matrix C=[Ci,j Ci-1,j Ci,j+1 Ci,j-1 Ci+1,j]

But how can calculate all the different values for C and how do I implement the boundary conditions?