% Advection Example 1
% numerical wave speeds

c = 1;
dx = .01;
x = 0:dx:5;
n = length(x);
u = zeros(1,n);
v = zeros(1,n);

R = .25;

dt = R*dx;
kmax = 1000;
t = 0:dt:(kmax-1)*dt;

for i=1:n
   u(i) = InC(x(i));
end
plot(x,u); axis([0 5 -0.1 1.1]);


for k=1:kmax-1
   v(1) = 0;
   v(n) = 0;
   for i=2:n-1
      v(i) = u(i) - R*(u(i)-u(i-1));
   end
   for i=1:n
      w(i) = InC(x(i)-c*t(k));
   end
   plot(x,v,x,w); axis([0 5 -0.1 1.1]);
   pause
   u = v;
end