# difference equation

## difference equation

[′dif·rəns i′kwā·zhən]
(mathematics)
An equation expressing a functional relationship of one or more independent variables, one or more functions dependent on these variables, and successive differences of these functions.

## 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.
References in periodicals archive ?
The multiple sine function satisfies the difference equation
The aim of this paper is to investigate the oscillatory behavior of even order nonlinear neutral difference equation
Szalkai  studied the max-type difference equation
For A(t), B(t) [member of] [C.sup.nxn](t) and [f.sub.n] [member of] [C.sup.n], the vector c [member of] [C.sup.n] is called a consistent initial vector for the difference equation A(t)[x.sub.n+1] = B(t)[x.sub.n] + [f.sub.n] if the initial value problem A(t)[x.sub.n+1] = B(t)[x.sub.n] + [f.sub.n], [x.sub.0] = c, n = 1,2, ..., has a solution for [x.sub.n].
The purpose of this paper is to extend some results for matrix difference equation obtained in  to the case of q-difference equations.
This is obtained by expanding each term of finite difference equation with the help of Taylor Series.
Difference equation appears as natural descriptions of observed evolution phenomena because most measurements of time evolving variables are discrete and so it arises in many physical problems, as nonlinear elasticity theory or mechanics, and engineering topics.
 investigated the qualitative behavior of the following second-order rational difference equation:
We consider the first order neutral advanced difference equation of the form

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