On the solutions of the Mathieu’s equation

Abstract

As shown in [1] solutions of the Mathieu’s equation were classified on three fundamental kinds depending mainly on its parameters. These solutions were constructed in the form of infinite series. This paper presents a new approach in which approximated analytical solutions of the Mathieu’s equation are constructed in the finite form. Depending on parameters of Mathieu’s equations general solutions may obtain following behaviors: either bounded almost periodic, or infinitely increased combining with infinitely decreased and or infinitely increased combining with periodic.