Lecture 25: Difference equations and multiple scales

Difference equations are analogous to differential equations, except that the the independent variables (which often represent space or time) are discrete rather than continuous. In this lecture, Prof. Strogatz discusses a difference equation arising from a time-discretization of a Duffing oscillator. The equation includes a small nonlinear term, and so is grist for perturbation theory. The lecture shows how the solution of this difference equation can be approximated asymptotically by using a discrete version of the method multiple scales.