difference equation

Equation involving differences between successive values of a function of a discrete variable (i.e., one defined for a sequence of values that differ by the same amount, usually 1).

A function of such a variable is a rule for assigning values in sequence to it. For example, f(x + 1) = xf(x) is a difference equation. Methods developed for solving such equations have much in common with methods for solving linear differential equations, which difference equations are often used to approximate.

* * *

      mathematical equality involving the differences between successive values of a function of a discrete variable. A discrete variable is one that is defined or of interest only for values that differ by some finite amount, usually a constant and often 1; for example, the discrete variable x may have the values x0 = a, x1 = a + 1, x2 = a + 2, . . . , xn = a + n. The function y has the corresponding values y0, y1, y2, . . . , yn, from which the differences can be found:

      Any equation that relates the values of Δyi to each other or to xi is a difference equation. In general, such an equation takes the form

      Systematic methods have been developed for the solution of these equations and for those in which, for example, second-order differences are involved. A second-order difference is defined as

 

* * *


Universalium. 2010.

Look at other dictionaries:

  • difference equation — skirtuminė lygtis statusas T sritis fizika atitikmenys: angl. difference equation vok. Differenzengleichung, f rus. разностное уравнение, n pranc. équation aux différences, f …   Fizikos terminų žodynas

  • difference equation — noun a) An equation involving an ordered sequence or real numbers () and some number if its differences, where the first difference is defined as and the k difference is defined recursively as . b) more broadly, any recurrence relation …   Wiktionary

  • Matrix difference equation — A matrix difference equation[1][2] is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. Occasionally …   Wikipedia

  • Difference operator — In mathematics, a difference operator maps a function, f ( x ), to another function, f ( x + a ) − f ( x + b ).The forward difference operator :Delta f(x)=f(x+1) f(x),occurs frequently in the calculus of finite differences, where it plays a role… …   Wikipedia

  • equation — /i kway zheuhn, sheuhn/, n. 1. the act of equating or making equal; equalization: the symbolic equation of darkness with death. 2. equally balanced state; equilibrium. 3. Math. an expression or a proposition, often algebraic, asserting the… …   Universalium

  • équation aux différences — skirtuminė lygtis statusas T sritis fizika atitikmenys: angl. difference equation vok. Differenzengleichung, f rus. разностное уравнение, n pranc. équation aux différences, f …   Fizikos terminų žodynas

  • Equation — E*qua tion, n. [L. aequatio an equalizing: cf. F. [ e]quation equation. See {Equate}.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night.… …   The Collaborative International Dictionary of English

  • Equation box — Equation E*qua tion, n. [L. aequatio an equalizing: cf. F. [ e]quation equation. See {Equate}.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the… …   The Collaborative International Dictionary of English

  • Equation clock — Equation E*qua tion, n. [L. aequatio an equalizing: cf. F. [ e]quation equation. See {Equate}.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the… …   The Collaborative International Dictionary of English

  • Equation of a curve — Equation E*qua tion, n. [L. aequatio an equalizing: cf. F. [ e]quation equation. See {Equate}.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the… …   The Collaborative International Dictionary of English

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.