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) = x f (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.