In mathematics, a recurrence relation is an equation that recursively defines a sequence, once one or more initial terms are given: each further term of the sequence is defined as a function of the preceding terms.
The term difference equation sometimes (and for the purposes of this article) refers to a specific type of recurrence relation. However, "difference equation" is frequently used to refer to any recurrence relation.
An example of a recurrence relation is the logistic map:
with a given constant r; given the initial term x0 each subsequent term is determined by this relation.
Some simply defined recurrence relations can have very complex (chaotic) behaviours, and they are a part of the field of mathematics known as nonlinear analysis.
Solving a recurrence relation means obtaining a closed-form solution: a non-recursive function of n.
Read more about Recurrence Relation: Fibonacci Numbers, Relationship To Differential Equations
Famous quotes containing the words recurrence and/or relation:
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—Samuel Johnson (1709–1784)
“We shall never resolve the enigma of the relation between the negative foundations of greatness and that greatness itself.”
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