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.