Perturbation theory approximates a problem depending on a small parameter 
by starting from the solvable problem
at 
and constructing an asymptotic series, commonly
of the form
 |
In a regular perturbation problem, this expansion is valid throughout the domain of interest. In a singular
perturbation problem, setting 
changes the character of the problem, and boundary
layers, the method of multiple scales,
or matched asymptotic expansions may be needed. Perturbation methods are used for
algebraic equations, differential equations,
eigenvalue problems, and dynamical
systems.
