Difference and functional equations Nonlinear difference equations Concept
Rational difference equation
Summary
A rational difference equation is a nonlinear difference equation whose next term is a quotient of two affine expressions in the earlier terms. It is one of the simplest classes of nonlinear recurrences, yet its solutions show convergence, periodicity and unbounded growth depending on the parameters. The first-order case is the iteration of a Möbius transformation and can be solved in closed form by reduction to a linear recurrence. Higher-order cases are studied mainly through the stability and periodicity of their solutions.
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| Tag | T8YDEASD1H |
|---|---|
| URI | m2://T8YDEASD1H |
| Kind | concept |
| Writing | W0 stub |
| MSC | 39A20, 39A05 |
| Specializes | Nonlinear difference equation |
| Same as |
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