Analytical Solution of Homogeneous Damped Mathieu Equation

Dmitri Yerchuck^1, , Alla Dovlatova², Yauhen Yerchak³ and Felix Borovik¹

¹Heat-Mass Transfer Institute of National Academy of Sciences of RB, Brovka Str., 15, Minsk, RB

²M.V.Lomonosov Moscow State University, Moscow

³Belarusian State University, Nezavisimosti Avenue 4, Minsk, RB

Cite this paper:
Dmitri Yerchuck, Alla Dovlatova, Yauhen Yerchak and Felix Borovik. Analytical Solution of Homogeneous Damped Mathieu Equation. International Journal of Physics. 2014; 2(5):165-169. doi: 10.12691/ijp-2-5-6

Abstract

The general solution of the homogeneous damped Mathieu equation in the analytical form, allowing its practical using in many applications, including superconductivity studies, without numerical calculations has been found.

Keywords:
Mathieu equation Bessel functions superconductivity

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Kim P W, de Graaf A M, Chen J T, Friedman E J, and Kim S H,Phase Reversal and Modulated Flux Motion in Superconducting Thin Films, Phys. Rev. B, 6, N 3 (1972) 887-893.
[2]	Kotowski G, Z.Angew. Math. Mech., 23 (1943) 213.
[3]	Meixner J and SchÄafke F W, Mathieusche Funktionen und SphÄaroidfunktionen, Springer, Berlin, 1954.
[4]	Bateman H,Erdelyi A, Higher Transcendental Functions, V.3, New York, Toronto, London, MC Graw-Hill Book Company, Inc., 1955, M., Nauka, 1967, 300 pp.
[5]	Mac Lachlan, Theory and Applications of Mathieu Functions, M., Izd.In.Lit., 1953, 476 pp.
[6]	Zaitsev V F, Polyanin A D, Hand-Book on Ordinary Differential Equations, M, Fizmatlit, 2001, 576 pp.