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

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

Аннотация

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.

Язык оригиналаанглийский
Название основной публикацииApplication of Mathematics in Technical and Natural Sciences
Подзаголовок основной публикации12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2020
РедакторыMichail D. Todorov, Michail D. Todorov
ИздательAmerican Institute of Physics
ISBN (электронное издание)9780735440364
DOI
СостояниеОпубликовано - 3 дек 2020
Событие12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - Albena, Болгария
Продолжительность: 24 июн 202029 июн 2020

Серия публикаций

НазваниеAIP Conference Proceedings
Том2302
ISSN (печатное издание)0094-243X
ISSN (электронное издание)1551-7616

конференция

конференция12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences
Сокращенный заголовокAMiTaNS 2020
СтранаБолгария
ГородAlbena
Период24/06/2029/06/20

Предметные области Scopus

  • Физика и астрономия (все)

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