Problem with Parabolic Linear PDE-crank-nicolson

Hi!

I am using crank nicolson method to implicitly solve a mass diffusion equation. Where a gas concentration above a 10cm column of water is held at C=.01mol/m3. The Diffusion constant is D=2*10^-9m2/s. Boundary conditions are assumed to be C=0 @ L=10cm. I am getting a resultant plot and solution but it doesn't necessarily make sense with what you would expect the results to be.

Any suggestions would be greatly appreciated!

 function  Crank 
% Parameters needed to solve the equation via Crank-Nicholson method 
timesteps = 100; % Number of time steps 
L =10.; % characteristic length cm
dt = .01; 
n = 50.; % Number of space steps 
dz = L/n; 
diffco = (2*10^-9)*10000*3600.*24.; % diffusion coefficient in days
xi = diffco*dt/(dz*dz); % Parameter of the method 
% Initial Concentration  
for i = 1:n+1 
 z(i) =(i-1)*dz; 
 u(i,1) =.01;
end 
% Concentration at the boundary (C=0) 
for k=1:timesteps+1 
 u(1,k) = 0; 
 u(n+1,k) = 0.; 
 time(k) = (k-1)*dt; 
end
% Defining the Matrices M_right and M_left in the method 
aL(1:n-2)=-xi; 
bL(1:n-1)=2.+2.*xi; 
cL(1:n-2)=-xi; 
MMl=diag(bL,0)+diag(aL,-1)+diag(cL,1);  
aR(1:n-2)=xi; 
bR(1:n-1)=2.-2.*xi; 
cR(1:n-2)=xi; 
MMr=diag(bR,0)+diag(aR,-1)+diag(cR,1); 
 % Implementation of the Crank-Nicholson method 
for k=2:timesteps % Time Loop 
 uu=u(2:n,k-1); 
 u(2:n,k)=inv(MMl)*MMr*uu; 
end 
% Graphical representation of the temperature at different selected times 
figure(1) 
plot(z,u)
title('Concentration-Crank-Nicholson method') 
xlabel('Z') 
ylabel('C') 
%u'
figure(2) 
mesh(z,time,u') 
title('Concentration within the Crank-Nicholson method') 
xlabel('Z') 
ylabel('Concentration')
  end

Answer 1

[zanubah adillah rahmah]

method crank nicolson delT/delt = k*del^2T/delx^2

Heat conduction in an aluminum rod long flat,

stem length L=10cm, delta x = 1 cm

time step, delta t = 0.1s

coefficient diffusion thermal, k = 0.835 cm^2/s

boundary conditions: T(x=0,t)= 100 celcius and T(x=20,t)=50 celcius

initial value: T(x,t=0)= 0 celcius