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On biorthogonal approximation of solutions of some boundary value problems on Shishkin mesh. / Kulikov, E.; Makarov, A.

Application of Mathematics in Technical and Natural Sciences: 12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2020. ed. / Michail D. Todorov; Michail D. Todorov. American Institute of Physics, 2020. 110005 (AIP Conference Proceedings; Vol. 2302).

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Harvard

Kulikov, E & Makarov, A 2020, On biorthogonal approximation of solutions of some boundary value problems on Shishkin mesh. in MD Todorov & MD Todorov (eds), Application of Mathematics in Technical and Natural Sciences: 12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2020., 110005, AIP Conference Proceedings, vol. 2302, American Institute of Physics, 12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, 24/06/20. https://doi.org/10.1063/5.0033812

APA

Kulikov, E., & Makarov, A. (2020). On biorthogonal approximation of solutions of some boundary value problems on Shishkin mesh. In M. D. Todorov, & M. D. Todorov (Eds.), Application of Mathematics in Technical and Natural Sciences: 12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2020 [110005] (AIP Conference Proceedings; Vol. 2302). American Institute of Physics. https://doi.org/10.1063/5.0033812

Vancouver

Kulikov E, Makarov A. On biorthogonal approximation of solutions of some boundary value problems on Shishkin mesh. In Todorov MD, Todorov MD, editors, Application of Mathematics in Technical and Natural Sciences: 12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2020. American Institute of Physics. 2020. 110005. (AIP Conference Proceedings). https://doi.org/10.1063/5.0033812

Author

Kulikov, E. ; Makarov, A. / On biorthogonal approximation of solutions of some boundary value problems on Shishkin mesh. Application of Mathematics in Technical and Natural Sciences: 12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2020. editor / Michail D. Todorov ; Michail D. Todorov. American Institute of Physics, 2020. (AIP Conference Proceedings).

BibTeX

@inproceedings{b269dfca20d64cbf916e09830d3e2555,
title = "On biorthogonal approximation of solutions of some boundary value problems on Shishkin mesh",
abstract = "Singularly perturbed boundary value problems are widely studied in applied problems of physicsand engineering. However, their solutions are rarely possible to construct in an explicit form, so numerical methods of solving such problems are actively studied. Functions that are the explicit orapproximate solution of this problem have huge boundary layer components; therefore, the application of classical interpolation methods leads to significant errors. This paper considers a piecewise-uniform Shishkin mesh, which allows improving the quality of approximation in the boundary layer. Alocal approximation scheme is implemented, minimal splines are used as basis functions, and the coefficients are calculated as de Boor-Fix type functional values, which are biorthogonal to minimalsplines. The results of numerical experiments are presented. They show that the discussed approximation method allows getting accurate approximations of functions that are the solutions of singularly perturbed boundary value problems, in comparison with previously published works. ",
author = "E. Kulikov and A. Makarov",
note = "Publisher Copyright: {\textcopyright} 2020 Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; 12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2020 ; Conference date: 24-06-2020 Through 29-06-2020",
year = "2020",
month = dec,
day = "3",
doi = "10.1063/5.0033812",
language = "English",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics",
editor = "Todorov, {Michail D.} and Todorov, {Michail D.}",
booktitle = "Application of Mathematics in Technical and Natural Sciences",
address = "United States",

}

RIS

TY - GEN

T1 - On biorthogonal approximation of solutions of some boundary value problems on Shishkin mesh

AU - Kulikov, E.

AU - Makarov, A.

N1 - Publisher Copyright: © 2020 Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/12/3

Y1 - 2020/12/3

N2 - Singularly perturbed boundary value problems are widely studied in applied problems of physicsand engineering. However, their solutions are rarely possible to construct in an explicit form, so numerical methods of solving such problems are actively studied. Functions that are the explicit orapproximate solution of this problem have huge boundary layer components; therefore, the application of classical interpolation methods leads to significant errors. This paper considers a piecewise-uniform Shishkin mesh, which allows improving the quality of approximation in the boundary layer. Alocal approximation scheme is implemented, minimal splines are used as basis functions, and the coefficients are calculated as de Boor-Fix type functional values, which are biorthogonal to minimalsplines. The results of numerical experiments are presented. They show that the discussed approximation method allows getting accurate approximations of functions that are the solutions of singularly perturbed boundary value problems, in comparison with previously published works.

AB - Singularly perturbed boundary value problems are widely studied in applied problems of physicsand engineering. However, their solutions are rarely possible to construct in an explicit form, so numerical methods of solving such problems are actively studied. Functions that are the explicit orapproximate solution of this problem have huge boundary layer components; therefore, the application of classical interpolation methods leads to significant errors. This paper considers a piecewise-uniform Shishkin mesh, which allows improving the quality of approximation in the boundary layer. Alocal approximation scheme is implemented, minimal splines are used as basis functions, and the coefficients are calculated as de Boor-Fix type functional values, which are biorthogonal to minimalsplines. The results of numerical experiments are presented. They show that the discussed approximation method allows getting accurate approximations of functions that are the solutions of singularly perturbed boundary value problems, in comparison with previously published works.

UR - http://www.scopus.com/inward/record.url?scp=85097838199&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/9f033bb3-a8c2-3da1-a71c-ad212d374443/

U2 - 10.1063/5.0033812

DO - 10.1063/5.0033812

M3 - Conference contribution

AN - SCOPUS:85097838199

T3 - AIP Conference Proceedings

BT - Application of Mathematics in Technical and Natural Sciences

A2 - Todorov, Michail D.

A2 - Todorov, Michail D.

PB - American Institute of Physics

T2 - 12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences

Y2 - 24 June 2020 through 29 June 2020

ER -

ID: 72078594