On the convergence of WKB approximations of the damped Mathieu equation
Journal of Mathematical Physics , Volume 62; doi:10.1063/1.5145267
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.
Keywords: WKB / convergence / Floquet / exponent / damped Mathieu equation
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