% Forward time, Centered space scheme 
% for diffusion equation with fixed BC

function utuxx_ftcx;

D = 2.02;
dt = 1;
dx = 2;
time = 400   % Time value to solve for
length = 50  % (L) Physical length of the metal wire

Ncells = length / dx + 1; % (m)
Nsteps = time / dt + 1;
L = D*dt/(dx)^2
  
u(Nsteps, Ncells) = 0;
u(1,:) = 25;       % initial condition (time=0)
u(:,1) = 0;        % left BC  (x=0)
u(:,Ncells) = 100; % right BC (x=L)

for n = 1:(Nsteps-1)
  
  for k = 2:(Ncells-1)
    u(n+1,k) = L*u(n,k-1) + (1-2*L)*u(n,k) + L*u(n,k+1);
  end

end

%figure
%surf(u(1:(Nsteps/12.5):Nsteps,1:(Ncells/12.5):Ncells));
%view(-154,26);
%figure;
plot(u(1:(Nsteps-1)/5:Nsteps,:)','.-');