difference equation from FOLDOC

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.