Chapter 4

Perturbation methods

Elementary boundary layer theory is described for linear second ordinary differential equations; the matching principle is described, and internal transition layers are analysed. A nonlinear boundary layer problem is then discussed, then weakly nonlinear oscillations via the Van der Pol oscillator, and lastly boundary layers for convection-diffusion equations.

The principal book for discussing perturbation methods is, in my view, that of Kevorkian and Cole (1982). The examples I have chosen are drawn from their book, because they are so pertinent and illuminate the principles beautifully. Readers who want to pursue this topic are advised to head straight for that text.