ABSTRACT
Owing to the complexity of the partial differential equations involved in some mathematical models, it is not always possible to find an exact solution to an initial/boundary value problem. The next best thing in such situations is to compute an approximate solution instead. This is the idea behind the method of asymptotic expansion, which is applicable to problems that contain a small positive parameter and relies on the expansion of the solution in a series of powers of the parameter. If the series converges, then the technique is called a perturbation method; when the series diverges but is asymptotic, then the technique is called an asymptotic method. This chapter discusses only the formal construction of the asymptotic series solution and obtains few terms, without considering the question of convergence. It examines a few specific models to how the perturbation method works for regular perturbation problems.
