On the convergence of WKB approximations of the damped Mathieu equation

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Author
Nwaigwe, D.
Affiliation
Program in Applied Mathematics, University of Arizona
Issue Date
2021

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Publisher
American Institute of Physics Inc.
Citation
Nwaigwe, D. (2021). On the convergence of WKB approximations of the damped Mathieu equation. Journal of Mathematical Physics, 62(6).
Journal
Journal of Mathematical Physics
Rights
Copyright © 2021 Author(s). Published under license by AIP Publishing.
Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
Abstract
The form of the fundamental set of solutions of the damped Mathieu equation is determined by Floquet theory. In the limit as m → 0, we can apply WKB theory to get first order approximations of the fundamental set. WKB theory states that this approximation gets better as m → 0 and T is fixed. However, convergence of the periodic part and characteristic exponent is not addressed. We show that they converge to those predicted by WKB theory. We also provide a rate of convergence that is not dependent on T. © 2021 Author(s).
Note
12 month embargo; published online: 01 June 2021
ISSN
0022-2488
DOI
10.1063/1.5145267
Version
Final published version
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