The governing equations of physical, biological and economic models often involve features which make it impossible to obtain their exact solution. Examples of such features are:

the occurrence of a complicated algebraic equation the occurrence of a complicated integral varying coefficients in a differential equation an awkwardly shaped boundary a nonlinear term in a differential equation

When a large or small parameter occurs in a mathematical model of a process there are various methods of constructing perturbation expansions for the solution of the governing equations. Often the terms in the perturbation expansions are governed by simpler equations for which exact solution techniques are available. Even if exact solutions cannot be obtained, the numerical methods used to solve the perturbation equations approximately are often easier to construct than the numerical approximation for the original governing equations.