clear;
clf;

N = 50;
L = 20.0;
h = L/N;
c = 1;
tau = h/c;
nstep = 50;

coef = c * tau / (2*h);

sig=0.1;                            % width of the pulse
z = ((1:N) - 1/2)*h - L/2;          % value of z at time 0
phi = (sech(z / (2 * sig^2))).^2;   % wave shape
phiset = zeros(nstep, N);

x = z;
t = 0:tau:(nstep - 1) * tau;
[xx, tt] = meshgrid(x, t);

for ist = 1:nstep
  phiset(ist,:) = phi;

  for k = 1:N
    if ( k ~= 1 ) && ( k ~= N )
      phinew(k) = (0.5-coef)*phi(k+1) + (0.5+coef)*phi(k-1);
    else
      phinew(1) = (0.5-coef)*phi(2) + (0.5+coef)*phi(N);
      phinew(N) = (0.5-coef)*phi(1) + (0.5+coef)*phi(N-1);
    end
  end
  phi = phinew;
end

surf(xx, tt, phiset);