Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
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).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
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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