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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 12, Pages 3–11 (Mi ivm9180)  
This article is cited in 14 scientific papers (total in 14 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
Full-text PDF (197 kB) Citations (14)
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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.
Received: 07.05.2015
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 12, Pages 1–8
DOI: https://doi.org/10.3103/S1066369X1612001X
Bibliographic databases:
Document Type: Article
UDC: 517.928+517.955
Language: Russian
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
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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