%  Flow in a Stream
clear;
%  Length of the Stream
L = 1.0;
%  Duration of Time
T = 20.;
K =800;
dt = T/K;
n = 80.;
dx = L/n;
vel = .1;
decay = .1;
%  Initial Concentration
for i = 1:n+1
	x(i) =(i-1)*dx;
	u(i,1) =sin(pi*x(i)*2);
end
%  Upstream Concentration
for k=1:K+1
	time(k) = (k-1)*dt;
	u(1,k) = sin(-pi*vel*time(k)*2)*exp(-decay*time(k));
end
%  Time Loop
for k=1:K
%  Space Loop
	for i=2:n+1;
		u(i,k+1) =(1 - vel*dt/dx -decay*dt)*u(i,k) + vel*dt/dx*u(i-1,k);
        error(i,k+1) = abs(sin(pi*(x(i)-vel*time(k))*2)*exp(-decay*time(k))-u(i,k));
	end
end
max(error(n+1,2:K+1))
mesh(x,time,u')