ABSTRACT
This chapter describes the study of perturbation expansions. It considers a model problem for which an exact solution is available against which the perturbation expansion can be compared. The chapter obtains expansions for the solution of polynomial equations involving small parameters. It also considers various initial value problems. This is followed by a study of expansions involving powers and inverse powers of the independent variable. These provide approximations for small and large values respectively of the independent variable. A feature of perturbation expansions is that they often form divergent series. The chapter also describes the concept of an asymptotic expansion, and demonstrates the value of a truncated divergent series. If a bound for the minimum remainder is not available but the expansion is known to be an asymptotic expansion then the best estimate is obtained by terminating the series when the terms begin to increase in magnitude. This is called the 'optimum truncation rule'.
