lsode precision

[Mario Maio]

I use lsode to solve a simple standard vibration problem with Octave 3.6.1:

function ydot=f(y,t) % 2nd order equation conversion to a 1st order system
    ydot(1)=y(2);
    ydot(2)=eqd(t,y(1),y(2));
end

function xdd = eqd(t,x,xd) % generic vibration
    m=1;
    K=1;
    omega=sqrt(K/m); % pulsazione naturale oscillatore
    fattore_smorzamento=0.07;
    S=2*fattore_smorzamento*m*omega;
    ampiezza_forzante=1;
    Omega=2.5; % pulsazione forzante
    forzante=ampiezza_forzante/m*sin(Omega*t);
    xdd=(-S*xd-K*x+forzante)/m;
end

y=lsode("f",[0;0],(t=(0:0.1:20*pi)'));
figure(1);plot(t,y(:,2))


But the result is qualitatively different from a manual Adam-Moulton 
corrector implementation which agrees with the text book the example was 
taken from.

Add the following code to the previous:

function [x,xd,xdd]=pred_corr(dt,tp,xp,xdp,xddp,tol)
    % tp, xdp, xddp are values of t, xd and xdd at previous step
    xddg=xddp; % as initial guess xdd is taken same as xddp
    for j=1:100
        xd=xdp+dt/2*(xddp+xddg);
        x=xp+dt/2*(xdp+xd);
        xdd=eqd(tp+dt,x,xd);
        if abs(xdd-xddg)<tol
            break;
        else
            xddg=xdd;
        end
    end
end

dt=.1;
tv=0:dt:20*pi;
t=tv(1);

x=0; % initial values
xd=0;

xdd=eqd(t,x,xd);

xv=[x];
for t=tv(1:end-1)
    [x,xd,xdd]=pred_corr(dt,t,x,xd,xdd,.000001);
    %display([t+dt x xd xdd])
    xv(end+1)=x;
end

figure(2);plot(tv,xv)


Is lsode unprecise? I have to change some settings to get more precision 
from lsode? (actually I already tried to change some settings but the 
result is the same)

Thanks.