function implicit_stability

h=.5;
t=0:h:100;

[l,m]=size(t);
x(1)=1;

for i=2:m
    x(i)=1/(1+h)*x(i-1);
end

M=max(abs(x));
if (M>1)
    M=10;
    Mi=-10;
else
    Mi=-1;
    M=1;
end

y=exp(-t);
figure(1)
plot(t,y,'r',t,x,'b')
title('implicit method')
axis([0 100 Mi M])