TY - JOUR

T1 - On approximate solution of one singular perturbation boundary value problem

AU - Kulikov, E. K.

AU - Makarov, A. A.

N1 - Publisher Copyright: © 2020 Saint-Petersburg State University. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - The paper considers the problem of approximation of a function that is a solution of singular perturbation boundary value problem. Such functions have huge boundary layer components, so the applying classical algorithms to them leads to essential errors. We introduce an approach that is a local approximation scheme based on minimal splines on the Shishkin grid, where coefficients of basis functions are calculated as the values of de Boor-Fix type functionals. We also present the results of numerical experiments showing that our approach allows obtaining the approximation of high quality.

AB - The paper considers the problem of approximation of a function that is a solution of singular perturbation boundary value problem. Such functions have huge boundary layer components, so the applying classical algorithms to them leads to essential errors. We introduce an approach that is a local approximation scheme based on minimal splines on the Shishkin grid, where coefficients of basis functions are calculated as the values of de Boor-Fix type functionals. We also present the results of numerical experiments showing that our approach allows obtaining the approximation of high quality.

KW - B-splines

KW - Boundary layer components

KW - De boor-fix type functionals

KW - Minimal splines

KW - Shishkin grids

UR - http://www.scopus.com/inward/record.url?scp=85097596493&partnerID=8YFLogxK

M3 - статья

AN - SCOPUS:85097596493

SP - 91

EP - 102

JO - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1817-2172

IS - 1

ER -