%% El viejo y querido (?) RK4 en el PVI para la ecuacion logistica

clear 
clc
close all

a = 1;
y0 = 0.1;
f = @(t,y) a*y*(1-y);

T = 5;
cant_pasos = 50;
h = T/cant_pasos;
y = zeros(1,cant_pasos+1);
y(1) = y0;


k1 = 0;
k2 = 0;
k3 = 0;
k4 = 0;

for n = 1:cant_pasos
    tn = h*(n-1);
    k1 = f(tn, y(n));
    k2 = f(tn+h/2, y(n) + h/2*k1);
    k3 = f(tn+h/2, y(n) + h/2*k2);
    k4 = f(tn+h, y(n) + h*k3);
    y(n+1) = y(n) + h*(k1 + 2*k2 + 2*k3 + k4) /6;
end

t = linspace(0,T,cant_pasos+1);
plot(t,exp(t*a)./(exp(t*a)+1/y0-1), '-k', 'LineWidth', 2)
hold on
plot(t,y, 'og','LineWidth',2)

% y(end)- exp(t(end)*a)./(exp(t(end)*a)+1/y0-1)