clear all;
%y(t+2) -4y(t-1)+ 16y(t) = 0, t>=0
%y(0) = 1, y(1) = 4*cos(pi/3);
t=[1:30];
y(1) = 1;
y(2) = 2;
for m=3:30;
    y(m)=4*y(m-1)-16*y(m-2);
end
stem(t,y,'o')
stem(t,y)
pause;
plot(t,y,'*')
pause
plot(t,y)
pause;
f = @(new_y) interp1(t,y, new_y, 'spline');
x=[1:.1:30];
for i = 1:291
ff(i)=f(x(i));
end
for i = 1:291
yte(i)=(4)^(x(i)-1)*(cos(pi/3*(x(i)-1)));
end
plot(x,ff,'r-',x,yte, 'b:')
xlabel ('tempo')
ylabel ('y')
title ('Curvas contínuas: spline (vermelha) e teórica (azul tracejado)')