function y = upwind()
 
 
 
N=100;
 %y = sparse(N,N);
 %sparse f(N-1,N-1);
dx = 1/(N-1);
x=[0:dx:1];
dt=dx/2;
t=[0:dt:1];
alpha=1;
u0=2;
lambda = u0 * dt/dx;
 y(1,:) = cos(2*pi*x);

 for n=1:N
     y(n,1) = alpha;
    for i=2:N
        y(n+1,i)= y(n,i) -lambda *(y(n,i)-y(n,i-1));           
    end
    plot(x,y(n,:),'blue');
    pause(0.1);
    %t(i)=(i-1)*dt;
    %y(i+1,1)= a;
end
%q2 steady state à 1 pour N = 435

%q3 on n'a pu la condition de CFL donc la courbe dépasse les conditions
%initiales (la coube explose)

sol = Yexfct(t,x);
err = norm (y(n+1,:)-sol(n+1,:))/norm (sol(n+1,:));