A method for evaluating Floquet characteristic exponents (FCE) of linear periodic (LP) systems has been developed in by Zhu and Vemula (1993), based on a so called harmonic balanced PD-characteristic equation. By iterating suitably modified such (nonlinear) equations using Newton's method, bifurcation diagrams are obtained which are shown to be the stability boundaries of the LP system. Illustrative examples are given for second-order Hill's equations. Owing to its computational efficiency and accuracy, the new method reveals nontrivial domains of stability for the classical Mathieu's equation which appear have been overlooked by previous researchers.
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