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.

Last updated: 1995-02-10