The majority of mathematical problems describing realistic systems cannot be solved exactly. They are therefore often solved by numerical methods .
Numerical solutions have, however, a number of draw-backs.
For one, it is usually quite difficult to get an overall impression of the dependence of the behavior of a system on its parameters. This type of information is readily available from analytical solutions. It is therefore often of great interest to obtain analytical solutions even if they solve the problem only approximately. In addition, the complete numerical solution often does not reveal which mechanisms are important for the understanding of a certain phenomenon and which are irrelevant. There are a number of standard asymptotic approaches that are used to consider certain limiting cases.