Source : Free On-Line Dictionary of Computing

difference equation
     
        A relation between consecutive elements of a sequence.  The
        first difference is
     
        	D u(n) = u(n+1) - u(n)
     
        where u(n) is the nth element of sequence u.  The second
        difference is
     
        	D2 u(n) = D (D u(n))
        		= (u(n+2) - u(n+1)) - (u(n+1) - u(n))
        		= u(n+2) - 2u(n+1) + u(n)
     
        And so on.  A recurrence relation such as
     
        	u(n+2) + a u(n+1) + b u(n) = 0
     
        can be converted to a difference equation (in this case, a
        second order linear difference equation):
     
        	D2 u(n) + p D u(n) + q u(n) = 0
     
        and vice versa.  a, b, p, q are constants.
     
        (1995-02-10)