Xo = 0;%lower limit
h = .01;%intervals
Xn = 2;%upper limit
y = 3.*exp(2.*Xo)./(exp(2.*Xo)+2);%the function at Xo
dy = 2.*(1-y./3).*y;%the derivative of y at Xo
%%%%%%%%%%%%%%%%Richardson%%%%%%%%%%%%%%%%%%%%%%%%%
%f = y;
%df = -f;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for x = h:h:Xn
    Y = y + h.*dy;%the value of the tangent line at x
%%%%%%%%%%%%%%%%Richardson%%%%%%%%%%%%%%%%%%%%%%%%%
    %F = f + 2.*h.*df;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    
    
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        func = 3.*exp(2.*x)./(exp(2.*x)+2);%actual function
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        %Error = func - Y;
        %Rel = Error/func;
 %%%%%%%%%%%%%%%%Richardson%%%%%%%%%%%%%%%%%%%%%%%%%
        %RError = 2.*Y - F;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%        
        [x, func, Y]
        
    y = Y;%function at Xn
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    dy = 2.*(1-y./3).*y;%derivative of y at Xn
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
    
%%%%%%%%%%%%%%%%Richardson%%%%%%%%%%%%%%%%%%%%%%%%%
    %f=F;
    %df = -f;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%      
end