clear all
exact_value=2/3;
for n=[64 128 256 512]  % n must be odd
    h=1/n;
    xg_h=0:h:1;
    y_h=(xg_h).^(1/2);
    tra_h = (h/2)*(y_h(1) + 2*sum(y_h(2:1:end-1)) + y_h(end));
    
    hh=2*h;
    xg_2h=0:hh:1;
    y_2h=(xg_2h).^(1/2);
    tra_2h = (h)*(y_2h(1) + 2*sum(y_2h(2:1:end-1)) + y_2h(end));
    
    p1=log2((exact_value-tra_2h)/(exact_value-tra_h));
    fprintf('n = %4d , h= % 1.7f , p1 = %1.7f\n',n,h,p1)
end