Periodic analytic approximate solutions for the Mathieu equation

Manuel Gadella (1) , Hector Giacomini (2) , Luis Lara

1 Departamento de Física Teórica, Atómica y Óptica
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

We propose two methods to find analytic periodic approximations intended for differential equations of Hill type. Here, we apply these methods on the simplest case of the Mathieu equation. The former has been inspired in the harmonic balance method and designed to find, making use on a given algebraic function, analytic approximations for the critical values and their corresponding periodic solutions of the Mathieu differential equation. What is new is that these solutions are valid for all values of the equation parameter q, no matter how large. The second one uses truncations of Fourier series and has connections with the least squares method.

Mots clés: Mathieu equation-periodic solution

Domaines: Systèmes dynamiques [math.DS]

Manuel Gadella, Hector Giacomini, Luis Lara. Periodic analytic approximate solutions for the Mathieu equation. Applied Mathematics and Computation, 2015, 271, pp.436-445. ⟨10.1016/j.amc.2015.09.018⟩. ⟨hal-01266871⟩