%%%%%%%%%%%%%%%%%%%%%%%%%
%diffuse.m
%
%solving a time-space problem for diffusion
%RK4 in time
%three-point centered difference in space
%
%Greg Gerbi
%24 April, 2012
%%%%%%%%%%%%%%%%%%%%%%%%%

dx = 0.01;
x = (-10:dx:10).';
lenx = length(x);
dt = 0.1;
t = (0:dt:1000).';
lent = length(t);

K = 1e-6;

%Dirichlet boundary condition
CB = 0;

%Initial conditions
C = zeros(size(x));
C(lenx./2) = 1;

for jn = 2:lent;
    d2Cdx2 = zeros(size(x));
    d2Cdx2(2:end-1) = (1./dx.^2) .* (C(1:end-2) - C(2:end-1) + C(3:end));
    %Dirichlet conditions
    d2Cdx2(1) = CB;
    d2Cdx2(end) = CB;
end