1d heat transfer

% solvediff.m

% Numerically solve the one dimensional diffusion equation

% Numerical method: central differential method

% 06/26/2009 created by Xiaozhou Zhou

X=linspace(0,1,101);                 % meshgrid

imax=length(X);                          % number of mesh elements

dx=X(2:end)-X(1:end-1);           % vector of element width

dxmin=min(dx);                          % minimum width

tttl=3;

dt=dxmin^2/4;                             % time step

nt=floor(tttl/dt);                            % number of time steps

T=0:dt:nt*dt;

C0 = zeros(1,imax);                  % initial condition

 C=C0; 

iout=1;

nout=10000;

Cs(iout,:)=C;

for it=1:nt

    C1=cds(C,imax-1,dx,dt);

    C=C1;

% boundary conditions

    C(1)=1;

    C(imax)=0;

% output

    if mod(it,nout)==0

        iout=iout+1;

        Cs(iout,:)=C1;

    end

end

% cds.m

% central differential method

function fun=cds(C,m,dx,dt)

fun=C;

for j=2:m

    fun(j)=C(j)+2*dt/(dx(j-1)+dx(j))*((C(j+1)-C(j))/dx(j)-(C(j)-C(j-1))/dx(j-1));

end