Singular perturbation methods

Abstract

In §6.2 in the last chapter we briefly discussed, by way of example, some singular perturbation problems in linear differential equations which could be solved using the exponential method developed there. In this chapter we discuss some more generally applicable singular perturbation techniques. These are extremely powerful and let us consider nonlinear problems, involving a small or large parameter, with a view to extracting the principle features of the solutions which cannot be found by classical methods. A fundamental property of nonlinear problems that we shall be interested in is that the main features of the solutions are not contained in the linearized problem as we see in §7.2 below.