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

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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.

Original languageEnglish
Title of host publicationApplication of Mathematics in Technical and Natural Sciences
Subtitle of host publication12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2020
EditorsMichail D. Todorov, Michail D. Todorov
PublisherAmerican Institute of Physics
ISBN (Electronic)9780735440364
DOIs
StatePublished - 3 Dec 2020
Event12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - Albena, Bulgaria
Duration: 24 Jun 202029 Jun 2020

Publication series

NameAIP Conference Proceedings
Volume2302
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences
Abbreviated titleAMiTaNS 2020
Country/TerritoryBulgaria
CityAlbena
Period24/06/2029/06/20

Scopus subject areas

  • Physics and Astronomy(all)

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