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Zh. Vychisl. Mat. Mat. Fiz., 2011, Volume 51, Number 8, Pages 1419–1433 (Mi zvmmf9523)  

Cauchy problem for the Mathieu equation away from parametric resonance

A. F. Kurin

Faculty of Physics, Voronezh State University, Universitetskaya pl. 1, Voronezh, 394006 Russia

Abstract: Four solutions of the Cauchy problem for Mathieu’s equation away from parametric resonance domains are analytically constructed using an asymptotic averaging method in the fourth approximation. Three solutions occur near fractional parameter values at which slow combination phases exist. The fourth solution occurs in the absence of slow phases away from parametric resonance domains and the fractional parameter values.

Key words: Cauchy problem, Mathieu equation, averaging method, amplitude, phase.

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English version:
Computational Mathematics and Mathematical Physics, 2011, 51:8, 1325–1338

Bibliographic databases:

UDC: 519.624.2
Received: 05.04.2010

Citation: A. F. Kurin, “Cauchy problem for the Mathieu equation away from parametric resonance”, Zh. Vychisl. Mat. Mat. Fiz., 51:8 (2011), 1419–1433; Comput. Math. Math. Phys., 51:8 (2011), 1325–1338

Citation in format AMSBIB
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\pages 1325--1338
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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