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    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
    
    Metadata
    Show full item record
    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
    ae974a485f413a2113503eed53cd6c53
    10.1063/1.5145267
    Scopus Count
    Collections
    UA Faculty Publications

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