Interpolation Formulas for Functions with Large Gradients in the Boundary Layer and their Application
Interpolation of functions on the basis of Lagrange’s polynomials is widely used. However in the case when the function has areas of large gradients, application of polynomials of Lagrange leads to essential errors. It is supposed that the function of one variable has the representation as a sum of...
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Yaroslavl State University
2016-06-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/353 |
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| author | A. I. Zadorin |
| author_facet | A. I. Zadorin |
| author_sort | A. I. Zadorin |
| collection | DOAJ |
| description | Interpolation of functions on the basis of Lagrange’s polynomials is widely used. However in the case when the function has areas of large gradients, application of polynomials of Lagrange leads to essential errors. It is supposed that the function of one variable has the representation as a sum of regular and boundary layer components. It is supposed that derivatives of a regular component are bounded to a certain order, and the boundary layer component is a function, known within a multiplier; its derivatives are not uniformly bounded. A solution of a singularly perturbed boundary value problem has such a representation. Interpolation formulas, which are exact on a boundary layer component, are constructed. Interpolation error estimates, uniform in a boundary layer component and its derivatives are obtained. Application of the constructed interpolation formulas to creation of formulas of the numerical differentiation and integration of such functions is investigated. |
| format | Article |
| id | doaj-art-e3bfbc060c2f45a48a07b94c3fb7205f |
| institution | DOAJ |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2016-06-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-e3bfbc060c2f45a48a07b94c3fb7205f2025-08-20T03:01:13ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172016-06-0123337738410.18255/1818-1015-2016-3-377-384310Interpolation Formulas for Functions with Large Gradients in the Boundary Layer and their ApplicationA. I. Zadorin0Sobolev Mathematics Institute SB RAS, Omsk department, 13 Pevtsova, 644043, Omsk, RussiaInterpolation of functions on the basis of Lagrange’s polynomials is widely used. However in the case when the function has areas of large gradients, application of polynomials of Lagrange leads to essential errors. It is supposed that the function of one variable has the representation as a sum of regular and boundary layer components. It is supposed that derivatives of a regular component are bounded to a certain order, and the boundary layer component is a function, known within a multiplier; its derivatives are not uniformly bounded. A solution of a singularly perturbed boundary value problem has such a representation. Interpolation formulas, which are exact on a boundary layer component, are constructed. Interpolation error estimates, uniform in a boundary layer component and its derivatives are obtained. Application of the constructed interpolation formulas to creation of formulas of the numerical differentiation and integration of such functions is investigated.https://www.mais-journal.ru/jour/article/view/353function of one variableboundary layer componentnonpolynomial interpolationquadrature formulasformulas of numerical differentiationerror estimate. |
| spellingShingle | A. I. Zadorin Interpolation Formulas for Functions with Large Gradients in the Boundary Layer and their Application Моделирование и анализ информационных систем function of one variable boundary layer component nonpolynomial interpolation quadrature formulas formulas of numerical differentiation error estimate. |
| title | Interpolation Formulas for Functions with Large Gradients in the Boundary Layer and their Application |
| title_full | Interpolation Formulas for Functions with Large Gradients in the Boundary Layer and their Application |
| title_fullStr | Interpolation Formulas for Functions with Large Gradients in the Boundary Layer and their Application |
| title_full_unstemmed | Interpolation Formulas for Functions with Large Gradients in the Boundary Layer and their Application |
| title_short | Interpolation Formulas for Functions with Large Gradients in the Boundary Layer and their Application |
| title_sort | interpolation formulas for functions with large gradients in the boundary layer and their application |
| topic | function of one variable boundary layer component nonpolynomial interpolation quadrature formulas formulas of numerical differentiation error estimate. |
| url | https://www.mais-journal.ru/jour/article/view/353 |
| work_keys_str_mv | AT aizadorin interpolationformulasforfunctionswithlargegradientsintheboundarylayerandtheirapplication |