clear all
clc

set(gca,'FontSize',18)
set(gca,'LineWidth',2)

name = 'burgers.gif';

eval(['delete ',name])


N = 1024;
x = linspace(-10,10,N);
delta_x = x(2) - x(1);
delta_k = 2*pi/(N*delta_x);

k = [0:delta_k:(N/2-1)*delta_k,0,-(N/2-1)*delta_k:delta_k:-delta_k];

u = zeros(size(x));
for n = 1:length(x);
    if (x(n) < 3) && (x(n) > -3)
        u(n) = 1;
    end
end

delta_t = 0.4/N;
t=0;
nu=0.1;
tmax = 10; nplt = floor((tmax/10)/delta_t); nmax = round(tmax/delta_t);
udata = u.'; tdata = 0;
U = fft(u);

plot(x,u,'LineWidth',2)
axis([-10,10,0,1.2])
xlabel('x')
ylabel('u')
text(6,0.7,'t=0.0','FontSize',18)
gif_add_frame(gcf,name,2);


for n = 1:nmax
    t = n*delta_t;
    % first do the linear part
    U = U.*exp(-nu*k.^2*delta_t);
    
    % then solve the nonlinear part
    
    U = U  - 1/2*(1i*k*delta_t).*fft((real(ifft(U))).^2);
    
    if mod(n,nplt) == 0
        u = real(ifft(U));
        udata = [udata u.']; tdata = [tdata t];
        plot(x,u,'LineWidth',2)
        axis([-10,10,0,1.2])
        xlabel('x')
        ylabel('u')
        text(6,0.7,['t=',num2str(t,'%0.1f')],'FontSize',18)
        gif_add_frame(gcf,name,2);
    end
end