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A method for constructing asymptotic expansions of bisingularly perturbed problems

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Abstract

In this paper we propose an analog of the method of boundary functions for constructing uniform asymptotic expansions of solutions to bisingularly perturbed problems. With the help of this method we construct uniform asymptotic expansions of solutions to the Dirichlet problem for bisingularly perturbed ordinary differential equations and elliptic equations of the second order. By the use of the maximum principle we obtain estimates for the remainder terms.

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Authors and Affiliations

  1. Osh State University, ul. Lenina 331, Osh, 723500, Republic of Kyrgyzstan

    K. Alymkulov

  2. Ural State Pedagogical University, ul. K. Libknekhta 9, Yekaterinburg, 620151, Russia

    D. A. Tursunov

Authors
  1. K. Alymkulov
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  2. D. A. Tursunov
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Correspondence to K. Alymkulov.

Additional information

Original Russian Text © K. Alymkulov, D.A. Tursunov, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 12, pp. 3–11.

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Alymkulov, K., Tursunov, D.A. A method for constructing asymptotic expansions of bisingularly perturbed problems. Russ Math. 60, 1–8 (2016). https://doi.org/10.3103/S1066369X1612001X

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  • DOI: https://doi.org/10.3103/S1066369X1612001X

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