Open AccessNew approaches to constructing quadrature formulas for functions with large gradients
Author(s) -
А. И. Задорин
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1901/1/012055
Subject(s) - quadrature (astronomy) , mathematics , numerical integration , clenshaw–curtis quadrature , tanh sinh quadrature , gauss–kronrod quadrature formula , polygon mesh , grid , minification , mathematical analysis , boundary value problem , gaussian quadrature , geometry , mathematical optimization , nyström method , engineering , electrical engineering
The problem of numerical integration of functions with large gradients in the boundary layer is studied. The use of the Newton-Cotes formulas on a uniform grid to integrate such functions can lead to significant errors. The article investigates approaches to the construction of quadrature formulas, the error of which does not increase due to large gradients of the function in the boundary layer. The following approaches are considered: the construction of quadrature formulas that are exact on the singular component responsible for the growth of the function in the boundary layer, the application of the Newton-Cotes formulas on the Shishkin and Bakhvalov meshes, minimization the error of the quadrature formula due to the construction of nodes. The investigated approaches are new, partially reflected in the publications. The results of computational experiments are presented.