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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 12, Pages 3–11 (Mi ivm9180)  

This article is cited in 8 scientific papers (total in 8 papers)

On a method of construction of asymptotic decompositions of bisingular perturbed problems

K. Alymkulova, D. A. Tursunovb

a Osh State University, 331 Lenin str., Osh, 723500 Republic of Кyrgyzstan
b Ural State Pedagogical University, 9 К. Libknekht str., Yekaterinburg, 620151 Russia

Abstract: We propose an analog of the method of boundary functions for constructing uniform asymptotic expansions of solutions to bisingular perturbed problems. With the use of this method we construct uniform asymptotic expansions of solutions to the Dirichlet problem for bisingular perturbed ordinary differential equations and second order elliptic equations. Applying the maximum principle, we obtain estimates for the remainder terms.

Keywords: asymptotic expansion, Dirichlet problem, Airy function, boundary functions.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:12, 1–8

Bibliographic databases:

UDC: 517.928+517.955
Received: 07.05.2015

Citation: K. Alymkulov, D. A. Tursunov, “On a method of construction of asymptotic decompositions of bisingular perturbed problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 12, 3–11; Russian Math. (Iz. VUZ), 60:12 (2016), 1–8

Citation in format AMSBIB
\by K.~Alymkulov, D.~A.~Tursunov
\paper On a~method of construction of asymptotic decompositions of bisingular perturbed problems
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 12
\pages 3--11
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 12
\pages 1--8

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    This publication is cited in the following articles:
    1. D. A. Tursunov, “Asimptoticheskoe reshenie bisingulyarnoi zadachi Robena”, Sib. elektron. matem. izv., 14 (2017), 10–21  mathnet  crossref
    2. 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
    3. 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
    4. D. A. Tursunov, “Asymptotic solving linear bisingular problems with additional boundary layer”, Russian Math. (Iz. VUZ), 62:3 (2018), 60–67  mathnet  crossref  isi
    5. D. A. Tursunov, “Asimptotika resheniya zadachi Dirikhle s singulyarnostyu vnutri koltsa”, Matematicheskaya fizika i kompyuternoe modelirovanie, 21:1 (2018), 44–52  mathnet  crossref
    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. K. G. Kozhobekov, D. A. Tursunov, “Asimptotika resheniya kraevoi zadachi, kogda predelnoe uravnenie imeet neregulyarnuyu osobuyu tochku”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:3 (2019), 332–340  mathnet  crossref
    8. Lipitakis A.-D., “the Numerical Solution of Singularly Perturbed Nonlinear Partial Differential Equations in Three Space Variables: the Adaptive Explicit Inverse Preconditioning Approach”, Mod. Simul. Eng., 2019 (2019), 5157145  crossref  isi
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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