A regular perturbation problem depends on a small parameter 
and has a solution expansion whose
successive terms remain valid throughout the domain of
interest as 
.
Setting 
leaves the type, order, and number of conditions of the original problem unchanged,
and the correction terms are ordinarily found from a sequence of problems of the
same general kind. This contrasts with a singular
perturbation, for which the limiting problem changes character and the expansion
is generally not uniform.
Regular Perturbation
See also
Asymptotic Series, Perturbation Theory, Singular PerturbationExplore with Wolfram|Alpha
References
Bender, C. M. and Orszag, S. A. Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory. New York: Springer-Verlag, 1999. https://doi.org/10.1007/978-1-4757-3069-2.Cite this as:
Weisstein, Eric W. "Regular Perturbation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RegularPerturbation.html