Abstract
In the method of matched asymptotic expansions studied in Chapter 2, the dependence of the solution on the boundary-layer coordinate was determined by solving the boundary-layer problem. In a similar way, when using multiple scales the dependence on the fast time scale was found by solving a differential equation. This does not happen with the WKB method because one begins with the assumption that the dependence is exponential. This is a reasonable expectation since many of the problems we studied in Chapter 2 ended up having an exponential dependence on the boundary-layer coordinate. Also, by making this assumption, we can significantly reduce the work necessary to find an asymptotic approximation of the solution.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Holmes, M.H. (1995). The WKB and Related Methods. In: Introduction to Perturbation Methods. Texts in Applied Mathematics, vol 20. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5347-1_4
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5347-1_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-5349-5
Online ISBN: 978-1-4612-5347-1
eBook Packages: Springer Book Archive