from
The Free On-line Dictionary of Computing (8 July 2008)
difference equation
<mathematics> 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)