clear,clc
% Solve ODE-IVP using Euler's Explicit Method
% y' = (x-1)(y-y^2)
% y(0) = 1/2
x0 = 0;
xEnd = 2;
y0 = 0.5;
h = 0.04; N = (xEnd - x0)/h

%% Initializing variables
X = [x0:h:xEnd]';
Y = zeros(N+1,1);
Y(1) = y0;
%ERR_GLOBAL = 0;
nodo = 0;
err_local = 0;
exact_value = 0;
aprox_value = 0;

% Exact solution of the EDO-PVI
A = 0.5*X.^2-X;
EXPO = exp(A);
YTrue = EXPO./(1+EXPO);

%% Solving using Euler's Explicit Method
for i = 1:N
  fi = (X(i)-1)*(Y(i)-Y(i)^2);
  nodo = X(i);
  Y(i+1) = Y(i) + h*fi;
  err_local = abs(Y(i+1)-Y(i))
  exact_value = YTrue(i+1);
  aprox_value = Y(i+1);
end
exact_value
aprox_value
% Error global
err_global = abs(exact_value - aprox_value)

%% Plot results and errors
plot(X,Y);
title('h=0.04, N=50');
xlabel('X'); ylabel('Y');
text (0.6, 0.46, "(MEE)E_{50}=|y(x_{50})-y_{50}|=0.010362");
legend ('Solucion aproximada');
hold on

plot(X,YTrue,'--r');
%ERR_GLOBAL = abs(YTrue - Y); %cálculo del error global
%MAX_ERR = max(ERR_GLOBAL)