clear all;
close all;

u_0   = 1.0;
t_0   = 0.0;
T        = 1.0;
%Dtmax    = 2.0/5.0;
Dtmax    = 0.25;
K        = ceil(T/Dtmax);
K        = K + 1;
Dt       = T/K;
tkmin    = linspace(t_0,t_0+T,K);
ukmin    = zeros(1,K);
ukmin(1) = u_0;

for k=1:K-1
  ukmin(k+1) = ukmin(k) + Dt*funz(tkmin(k),ukmin(k));
end

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
  uk(k+1) = uk(k) + Dt*funz(tk(k),uk(k));
end


figure(1)
handle = axes
set(handle,'FontSize',18)
handle = plot(tkmin,ukmin,'--',tk,uk,'-');
set(handle,'LineWidth',5);
grid on
xlabel('t')
ylabel('u')
%legend('\Deltat=0.4','\Deltat=0.01')
legend('\Deltat=0.25','\Deltat=0.01')