// Equation de la chaleur
clear; close;da=gda(); da.auto_clear='on';

T=0.1;	// temps final
cfl=0.5;
	
N=[20,40,80,160];	// Nb de point de discretisation
erreur=[];
for n=N
	dx=1/n;
	dt=cfl*dx^2/2.
	x=linspace(0,1,n+1);
	//u0=(1.-4.*((x-0.5)^2))';
	u0=cos(%pi*x)';
	u=u0;
	A=diag(sparse(2.*ones(1,n+1)))-diag(sparse(ones(1,n)),1)-diag(sparse(ones(1,n)),-1);
	A(1,2)=-2.;
	A(n+1,n)=-2.;
	A=A/(dx)^2;
	for t=dt:dt:T,
		u=u-dt*A*u;//schéma explicite
		//	plot2d(x,[u u0]);
	end;
	uexact=exp(-%pi^2*t)*cos(%pi*x)';
	erreur=[erreur,sqrt(((u-uexact)'*(u-uexact)*dx))];
end;
dN=ones(N)./N;
dN2=ones(N)./(N^2);
plot2d(N,[erreur',dN',dN2'],logflag='ll');