// convection: schéma de Lax-Wendroff
clear; close, da=gda(); da.auto_clear='on';

V=1;    // vitesse de convection
T=1;    // temps final  
cfl=0.5;
a=0;b=1;
        
function y=u0(x)
        y=double(x<0.5);
endfunction
        
N=[20,40,80,160,500];       // Nb de point de discretisation
erreur=[];      
for n=N         
        dx=1/n;
        dt=cfl*dx/V;
        x=linspace(a,b,n+1);
        u=u0(x)';
        for t=dt:dt:T,
                u=(1-cfl^2)*u-0.5*(cfl-cfl^2)*[u(2:n+1);u(2)]+0.5*(cfl+cfl^2)*[u(n);u(1:n)];    // Law Wendroff
                //plot2d(x,u);
        end;
        uexact=u0(x)';	// solution periodique
//        plot2d(x,[u uexact]);
        erreur=[erreur,sqrt(((u-uexact)'*(u-uexact)-(u(1)-uexact(1))^2)*dx)];
end;
Dx38=ones(N)./(N^(3/8));
plot2d(N,[erreur',Dx38'],logflag='ll');