On the convergence of WKB approximations of the damped Mathieu equation
AffiliationProgram in Applied Mathematics, University of Arizona
MetadataShow full item record
PublisherAmerican Institute of Physics Inc.
CitationNwaigwe, D. (2021). On the convergence of WKB approximations of the damped Mathieu equation. Journal of Mathematical Physics, 62(6).
JournalJournal of Mathematical Physics
RightsCopyright © 2021 Author(s). Published under license by AIP Publishing.
Collection InformationThis 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 email@example.com.
AbstractThe 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).
Note12 month embargo; published online: 01 June 2021
VersionFinal published version