This article is cited in 15 papers

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

K. Alymkulov^a, D. A. Tursunov<sup>b

a</sup> 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.

UDC: 517.928+517.955

Received: 07.05.2015

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

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