Solving First Order PDEs

Hi, I have been trying to solve a set of PDE equations in MATLAB, but I have first order PDE equations in my system which I don't know how to solve in MATLAB. However, I could solve the second order PDE based on many examples I found over the net. I have attached the equations. Any help would be greatly appreciated on how to solve first order PDEs in MATLAB.

Thanks in advance.

Answer 1

[Torsten]

If

0=z(1)<z(2)<...<z(N)=H

is a discretization in z-direction, approximate

dT_g/dz (z(i)) = (T_g(z(i))-T_g(z(i-1)))/(z(i)-z(i-1))
dT_l/dz (z(i)) = (T_l(z(i+1))-T_l(z(i)))/(z(i+1)-z(i))

Then solve the resulting system of ordinary differential equations using ODE15S, e.g..

Look up "method of lines".

Best wishes

Torsten.