format compact; clear all;

h = .01      % STEPSIZE
N = 1000    % NUMBER of ITERATIONS

y(1)=3;       % INITIAL CONDITIONS
z(1)=3;
t(1)=0;

% EULER'S METHOD

for i=1:N
    y(i+1) = y(i) + h*2*(1-y(i))
    t(i+1) = i*h;
end

% 2-nd ORDER RUNGE_KUTTA METHOD

for i=1:N
    f1 = h*2*(1 - z(i));
    f2 = h*2*( 1 - z(i) - f1 );
    z(i+1) = z(i) + (f1+f2)/2;
end

figure;
hold on;
plot(t,z,'LineWidth',2,'Color',[1 0 1]);
plot(t,y,'LineWidth',2);
fplot('1+2*exp(-2*x)',[0,10],'k');
legend('RUNGE-KUTTA APPROXIMATION','EULER APPROXIMATION','ACTUAL SOLUTION',3)
[t,q]=meshgrid(0:.2:9.8,0:.15:3);
dt = ones(21,50);
dq = 2*(1-q);
quiver(t,q,dt,dq,1);