clear all;clc;


a  = 2; % syntelestis tou ekthetikou
x0 = 1; % i arxiki synthiki

% ftiaxno to dianysma me tis xronikes stigmes
d  = 0.1;
tf = 2;
T  = [0:d:tf];


% ftiaxno ta dianysmata pou tha balo tis lyseis
X_eul = 0*T;  % se afto tha mpei i lysi me Euler
X_rk4 = 0*T;  % se afto tha mpei i lysi me Runge-Kutta



% edo arxizei to loop tis EULER
X_eul(1) = x0;
for it=2:length(T)
    x =X_eul(it-1);
    X_eul(it) = x + d * Xdot(x,a);
end


% edo arxizei to loop tis RUNGE-KUTTA
X_rk4(1) = x0;
for it=2:length(T)
    x = X_rk4(it-1);
    k1 = Xdot(x,a);
    k2 = Xdot(x+k1*d/2,a);
    k3 = Xdot(x+k2*d/2,a);
    k4 = Xdot(x+k3*d,a);
    
    X_rk4(it) = x + d * (k1+2*k2+2*k3+k4)/6; 
end


% i analytiki lysi
Xtheor = x0*exp(a*T);


% zografizo tis 3 lyseis (Euler, RK4, analytiki)
figure(3)
plot(T,X_eul,'b',T,X_rk4,'g',T,Xtheor,'--r')