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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 3, Pages 414–423 (Mi zvmmf314)  

This article is cited in 3 scientific papers (total in 4 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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:3, 397–406

Bibliographic databases:

UDC: 519.624.2+517.589
Received: 03.10.2006

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
\Bibitem{AbrKur07}
\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://www.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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. K. Kerimov, “On the 85th birthday of Aleksandr Aleksandrovich Abramov”, Comput. Math. Math. Phys., 51:10 (2011), 1653–1658  mathnet  crossref  mathscinet  isi
    2. Chuiko S.M., Starkova O.V., “Modifitsirovannaya dvukhshagovaya iteratsionnaya tekhnika dlya postroeniya funktsii mate”, Kompyuternye issledovaniya i modelirovanie, 4:1 (2012), 31–43  elib
    3. S. M. Chuiko, O. V. Starkova, “Modifitsirovannaya dvukhshagovaya iteratsionnaya tekhnika dlya postroeniya funktsii Mate”, Kompyuternye issledovaniya i modelirovanie, 4:1 (2012), 31–43  mathnet  crossref
    4. Rozhdestvenskii Yu.V., Rudyi S.S., “Linear Ion Trap With a Deterministic Voltage of the General Form”, Tech. Phys., 62:4 (2017), 625–632  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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