Equation resolution

Hi,

I would like to write this equation in Matlab :

A (dC/dt)+ B (dC/dz)=0

with these conditions :

for t=0 and z>0 : C=C0, for z=0 and t>0 : C=0, for z=L and t>0 : dC/dz=0,

and how to resolve it. thanks for your help in advance

[Walter Roberson]

You have not defined the results for t=0 z=0

Answer 1

[Clemens]

I also only see the trivial solution C(z,t) = 0

But let me take some notes and see if a something more general is possible.

Let's write as product: C(z,t) = f(z)g(t) then you got the boundary conditions:

z>0: g(0) = 0; 
t>0: f(0)=0; 
     f'(L) =0;

Then you could choose f any function that solves these conditions.

and solve g...

A f(z) g'(t) + B f'(z) g(t) == 0

simplify to

g'(t) = - B/A f'(z)/f(z) g(t)

So the general solution would be:

g(t) = D * exp(-B/A f'/f t)

but with g(0)=0 it requires D=0

unless one is nitpicking...

• if A=0 and B=0 - you are free to choose g to anything that fullfills the boundaries.
• what if only one is 0: then either g(t)=0 or g'(t) = 0. Both together with your boundary lead to C(z,t) = 0.
• maybe if f=0 or f'=0... no then the outcome for C would C(z,t) = 0
• well actually if you construct f such that it is 0 in the range [0,L] then you could solve g without any more conditions.
• and/or if you make g such that it is 0 for t >=0 you are free to solve f analogous.

but reading the question I think the interesting area would be t>0 and z=[0,L]. So only C(z,t) = 0 in that range.

Or someone with better math skills comes for help :D

[mouna]

thanks for your help

but g(0)isn't =0 i have g(0) =C0 that's why D=C0

i'm very sorry but this the first time that i use matlab,i have a project and i need a programmation with matlab and until now i don't know how to write this equation with these conditions in algorithm in matlab.i need really a help!!!!!!!!!!!!!

thanks for your help in advance

[Clemens]

First things first. When you say "write" there are several ways depending on what you want.

I suppose you are after a numerical solution. You can use bvp4c for that. There is an example in the help.

You can also input it symbolicaly. But I never used that, so no help from me there.

But keep in mind the first post. f is not uniquely defined. So you might get many different solutions.

Answer 2

[Walter Roberson]

Solution: C0 = 0, C(z,t) = 0

[mouna]

hi,

for t=0 and z=0:C=0

this is the first time I use matlab

and I do not know how I can write +(and resolve)this equation in matlab

thanks for your help in advance