clear all;
close all;

ITERMAX = 1000;
TOL_u = 1.0E-8;

u_0   = 1.0;
t_0   = 0.0;
T        = 1.0;
K     = 101;
Dt    = T/(K-1);
tk    = linspace(t_0,t_0+T,K);
uk    = zeros(1,K);
uk(1) = u_0;

for k=1:K-1
  ukk = uk(k);
  for i=1:ITERMAX
    uk(k+1) = g2(tk(k+1),uk(k),ukk,Dt);

    if( abs(uk(k+1)-ukk)<TOL_u )
      iter(k) = i;
      break;
    else
      ukk = uk(k+1);
    end
  end
end


figure(1)
handle = axes
set(handle,'FontSize',18)
handle = plot(tk,uk,'-');
set(handle,'LineWidth',5);
grid on
xlabel('t')
ylabel('u')


figure(2)
handle = axes
set(handle,'FontSize',18)
handle = plot(iter,'--');
set(handle,'LineWidth',5);
axis([1 K-1 0 (max(iter)+1)])
grid on
xlabel('k')
ylabel('iterazioni')