ABSTRACT
In this chapter, we introduce another asymptotic method for solving singularly perturbed problems called the WKB approximation, named after the physicists Gregor Wentzel, Hendrik Kramers, and Léon Brillown, who all developed it in 1926. This approximation is considered to be the most powerful tool for obtaining global approximations to the solutions of singularly perturbed equations but is applicable only to linear differential equations. Although this method was developed basically for solving singularly perturbed problems, it can be used to solve unperturbed problems as well. Note also that the problems involving large parameters and the problems for which we have to find solutions at irregular singular points (IRSPs) also can be solved easily using this method (see Example 6.1 of this chapter). In addition, problems with rapidly oscillating solutions can be solved using this method (Bender and Orszag, 1999).
