%
%   Script to iterate a difference equation and check against exact solution
%
%
%   First enter the right number of initial conditions (note MATLAB array
%   indices must start at 1; this has the effect that n must be changed to
%   (n-1) in the formula for the exact solution):
%
x(1)=1;
x(2)=2;
phi=pi/4;              % (For exact solution)
tworoot2=2*sqrt(2);    % (Ditto)
for n=3:20
  x(n)=4*x(n-1)-8*x(n-2);
  exact=tworoot2^(n-1)*cos((n-1)*phi);
  fprintf('n: %4i   FDE: %10.6g   Formula: %10.6g\n',n,x(n),exact)
end