% solution of x'=x(1-x) using 
% Euler's algorithm (x)
% 2nd order Taylor (y)
% 2nd order RK (z)

function ode

init = 1.2; % initial condition
h = 1;      % step size
tm = 10;     % time value

x(1) = init;
y(1) = init;
z(1) = init;
t(1) = 0;

for i=1:(tm/h)
    % Euler
    x(i+1) = x(i) + h*x(i)*(1-x(i));
    % 2nd order Taylor
    y(i+1) = y(i) + h*y(i)*(1-y(i)) + (h^2/2)*(1-2*y(i))*y(i)*(1-y(i));
    % 2nd order RK
    K1 = h * z(i) * ( 1 - z(i) );
    K2 = h * (z(i)+K1) * (1 - (z(i)+K1) );
    z(i+1) = z(i) + ( K1 + K2 )/2;
   
    t(i+1) = t(i) + h;   
end 

plot(t,x,t,y,t,z)
legend('Euler','2nd order Taylor','2nd order RK')