% ddwave3.m
% Inviscid Burgers equation
% First-order up-winding finite volume method.

L  = 10;
N  = 100;
x  = linspace(0,L*((N-1)/N),N);

k  = 2*pi/5;
%un = .4*sin(k*x);
un  =.5* exp(-(x-L/2).^2);
dx = x(2)-x(1);
nu = 0.5;
dt = nu*dx/1;
n  = 0;
u  = un;
us = un;
gu = un;
phi= un;
axn = [0 L -1.2 1.2];
plot(x,u), axis(axn), drawnow

while (n*dt < 20)
    % Up winding first order
    for i=1:N-1
        chat = 0.5*(u(i)+u(i+1));
        if chat > 0 
            F(i)=0.5*(u(i))^2;
        else
            F(i)=0.5*(u(i+1))^2;
        end
        if (u(i) < 0) && (u(i+1) > 0)
            F(i) =-0.5*(u(i))*(u(i+1));
        end
    end    
    chat = 0.5*(u(N)+u(1));
    if chat > 0 
            F(N)=0.5*(u(N))^2;
    else
            F(N)=0.5*(u(1))^2;
    end
    if (u(N) < 0) && (u(1) > 0)
            F(N) =-0.5*(u(N))*(u(1));
    end
    
     
 
    u  = u - (dt/dx)*(F - circshift(F,[0 1]));   
    n=n+1;
    plot(x,u), axis(axn),drawnow,title(n*dt)
   %n*dt
    %pause(.05)
end
    plot(x,u), axis(axn),drawnow
    max(u)