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Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 1, Pages 271–281 (Mi timm1280)  

This article is cited in 7 scientific papers (total in 7 papers)

Asymptotic expansion for a solution of an ordinary second-order differential equation with three turning points

D. A. Tursunov

Urals State Pedagogical University, Ekaterinburg

Abstract: Using the generalized method of boundary functions, we construct a uniform asymptotic expansion of the solution of the Dirichlet problem for a singularly perturbed linear inhomogeneous ordinary second-order differential equation with three turning points on the real axis. The constructed asymptotic series is a Puiseux series.

Keywords: asymptotic expansion, turning point, singular (bisingular) perturbation, ordinary second-order differential equation, Airy equation, modified Bessel functions, Dirichlet problem, generalized boundary function, small parameter.

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Bibliographic databases:
UDC: 517.928
Received: 07.04.2015

Citation: D. A. Tursunov, “Asymptotic expansion for a solution of an ordinary second-order differential equation with three turning points”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 271–281

Citation in format AMSBIB
\Bibitem{Tur16}
\by D.~A.~Tursunov
\paper Asymptotic expansion for a solution of an ordinary second-order differential equation with three turning points
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 1
\pages 271--281
\mathnet{http://mi.mathnet.ru/timm1280}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3497204}
\elib{https://elibrary.ru/item.asp?id=25655618}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. A. Tursunov, U. Z. Erkebaev, E. A. Tursunov, “Asimptotika resheniya zadachi Dirikhle dlya koltsa s kvadratichnymi rostami na granitsakh”, Izv. IMI UdGU, 2016, no. 2(48), 73–81  mathnet  elib
    2. D. A. Tursunov, “Asimptoticheskoe reshenie bisingulyarnoi zadachi Robena”, Sib. elektron. matem. izv., 14 (2017), 10–21  mathnet  crossref
    3. D. A. Tursunov, K. G. Kozhobekov, “Asimptotika resheniya singulyarno vozmuschennykh differentsialnykh uravnenii s drobnoi tochkoi povorota”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 21 (2017), 108–121  mathnet  crossref
    4. D. A. Tursunov, “The asymptotic solution of the three-band bisingularly problem”, Lobachevskii J. Math., 38:3, SI (2017), 542–546  crossref  mathscinet  zmath  isi  scopus
    5. D. A. Tursunov, “Asymptotic solving linear bisingular problems with additional boundary layer”, Russian Math. (Iz. VUZ), 62:3 (2018), 60–67  mathnet  crossref  isi
    6. D. A. Tursunov, K. G. Kozhobekov, “Asimptoticheskoe reshenie singulyarno vozmuschennoi zadachi Koshi s tochkoi povorota”, Matematicheskii analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 156, VINITI RAN, M., 2018, 84–88  mathnet
    7. D. A. Tursunov, M. O. Orozov, “Asimptoticheskoe reshenie zadachi Dirikhle dlya koltsa, kogda sootvetstvuyuschee nevozmuschennoe uravnenie imeet regulyarnuyu osobuyu okruzhnost”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2020, no. 63, 37–46  mathnet  crossref
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