% Compute u(n) using the recursive formula
%   u(n+2) = 3*u(n+1) - 2*u(n)
% with initial values
%   u(1) = 0.1,   u(2) = 0.1
% In exact arithmetic, the answer should be
%   u(n) = 0.1  for all n
% However, in finite precision arithmetic,
% we can see the instability.

% allocate memory for a 100-dim vector u
u = zeros(100,1);

% set the first two elements
u(1) = 0.1;
u(2) = 0.1;

% do the iteration
for n = 1:98
  u(n+2) = 3*u(n+1) - 2*u(n);
end

% draw the result
plot(u)

% print out several values
u(10)
u(50)
u(100)

ans =

    0.1000


ans =

    0.1078


ans =

   8.7961e+12

Published with MATLAB® 7.6