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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 3, Pages 414–423 (Mi zvmmf314)  
This article is cited in 6 scientific papers (total in 7 papers)

Calculation of solutions to the Mathieu equation and of related quantities

A. A. Abramov, S. V. Kurochkin

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
Full-text PDF (1281 kB) Citations (7)
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Abstract: For the Mathieu equation, we consider finding eigenvalues with a given index (on the basis of oscillation theorems for the relevant difference equations), the stability of solutions to the difference equations, correct definition and calculation of eigenvalues and Mathieu functions with noninteger numbers, correct definition and calculation of the Mathieu characteristic exponent, and the calculation of values of solutions to the Mathieu equation for large arguments. Numerical algorithms are proposed for the problems listed above.
Key words: Mathieu functions, oscillation theorems, recurrences, numerical stability.
Received: 03.10.2006
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 3, Pages 397–406
DOI: https://doi.org/10.1134/S0965542507030050
Bibliographic databases:
Document Type: Article
UDC: 519.624.2+517.589
Language: Russian
Citation: A. A. Abramov, S. V. Kurochkin, “Calculation of solutions to the Mathieu equation and of related quantities”, Zh. Vychisl. Mat. Mat. Fiz., 47:3 (2007), 414–423; Comput. Math. Math. Phys., 47:3 (2007), 397–406
Citation in format AMSBIB
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\by A.~A.~Abramov, S.~V.~Kurochkin
\paper Calculation of solutions to the Mathieu equation and of related quantities
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 3
\pages 414--423
\mathnet{http://mi.mathnet.ru/zvmmf314}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2348291}
\zmath{https://zbmath.org/?q=an:05200990}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 3
\pages 397--406
\crossref{https://doi.org/10.1134/S0965542507030050}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34247147749}
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  • https://www.mathnet.ru/eng/zvmmf/v47/i3/p414
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:75
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