 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.
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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 x_{0} = a, x_{1} = a + 1, x_{2} = a + 2, . . . , x_{n} = a + n. The function y has the corresponding values y_{0}, y_{1}, y_{2}, . . . , y_{n}, from which the differences can be found:Any equation that relates the values of Δy_{i} to each other or to x_{i} is a difference equation. In general, such an equation takes the formSystematic methods have been developed for the solution of these equations and for those in which, for example, secondorder differences are involved. A secondorder difference is defined as* * *
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