numx = 101;   %number of grid points in x
numt = 2000;  %number of time steps to be iterated
dx = 1/(numx - 1);
dt = 0.00005;

x = 0:dx:1;   %vector of x values, to be used for plotting

C = zeros(numx,numt);   %initialize everything to zero

%specify initial conditions
t(1) = 0;      %t=0
mu = 0.5;      
sigma = 0.05;
for i=1:numx
   C(i,1) = exp(-(x(i)-mu)^2/(2*sigma^2)) / sqrt(2*pi*sigma^2);
end

%iterate difference equations
for j=1:numt
   t(j+1) = t(j) + dt;
   for i=2:numx-1
      C(i,j+1) = C(i,j) + (dt/dx^2)*(C(i+1,j) - 2*C(i,j) + C(i-1,j)); 
   end
   C(1,j+1) = C(2,j+1);          %C(1,j+1) found from no-flux condition
   C(numx,j+1) = C(numx-1,j+1);  %C(numx,j+1) found from no-flux condition
end

figure(1);
hold on;
plot(x,C(:,1));
plot(x,C(:,11));
plot(x,C(:,101));
plot(x,C(:,1001));
plot(x,C(:,2001));
xlabel('x');
ylabel('c(x,t)');

%calculate approximation to the integral of c from x=0 to x=1
for j=1:numt+1
   s(j) = sum(C(1:numx-1,j))*dx;
end

figure(2);
plot(t,s);
xlabel('t');
ylabel('c_{total}');
axis([0 0.1 0.9 1.1]);