clear all;
%y(t+2) + 0.25y(t) = 5, t>=0
%y(0) = 5, y(1) = 4,5
t=[1:30];
y(1) = 5;
y(2) = 4.5;
for m=3:30;
    y(m)=-0.25*y(m-2)+5;
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)=(0.5)^(x(i)-1)*(cos(pi/0.5*(x(i)-1))+sin(pi/0.5*(x(i)-1))) + 4;
end
plot(x,ff,'r-',x,yte, 'b:')
xlabel ('tempo')
ylabel ('y')
title ('Curvas contínuas: spline (vermelha) e teórica (azul tracejado)')
pause;
clear yte;
x2=[1:.4:30];
for i = 1:73
yte(i)=(0.5)^(x(i)-1)*(cos(pi/0.5*(x(i)-1))+sin(pi/0.5*(x(i)-1))) + 4;
end
plot(x,ff,'r-',x2,yte, 'b:')
xlabel ('tempo')
ylabel ('y')
title ('Curvas contínuas: spline (vermelha) e teórica (azul tracejado)')