difference equation

difference equation

[′dif·rəns i′kwā·zhən]
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 purpose of this paper is to extend some results for matrix difference equation obtained in [4] to the case of q-difference equations.
For the transitional node in the interior domain, the weighted average method will also be used to formulate its finite difference equation, but more weight parameters will be introduced, when compared to the method proposed in [24].
This is obtained by expanding each term of finite difference equation with the help of Taylor Series.
The solution of the diffusion equation by a high order correct difference equation J.
2-8) and the standard (1) were calculated using the CIE 1976 color difference equation ([DELTA][E.
The first-order vector stochastic difference equation expresses the next period's vector of state variables as a linear function of this period's state vector and a vector of random disturbances that form a martingale difference sequence, to the system.
HAM has been applied successfully to obtain the series solution of various types of linear and nonlinear differential equations such as the viscous flows of non-Newtonian fluids [3-13], the KdV-type equations [14-16], nanoboundary layer flows [17], nonlinear heat transfer [18, 19], finance problems [20, 21], Riemann problems related to nonlinear shallow water equations [22], projectile motion [23], Glauert-jet flow [24], nonlinear water waves [25], ground water flows [26], Burgers-Huxley equation [27], time-dependent Emden-Fowler type equations [28], differential difference equation [29], difference equation [30], Laplace equation with Dirichlet and Neumann boundary conditions [31], and thermal-hydraulic networks [32].
We consider the first order neutral advanced difference equation of the form
Relationship (1) should be replaced by second order difference equation.
Proof Applying into 15 and 16, the roots of the difference equation are:
It is well known that exponential decay of the solution of a linear autonomous ordinary differential equation (ODE) x'(t) = Ax(t), t [member of] R or of an autonomous difference equation (O[DELTA]E) x(n +1) = Ax(n), n [member of] Z, can be characterized by spectral properties of A.

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