Open AccessThe error estimates of Kronrod extension for Gauss-Radau and Gauss-Lobatto quadrature with the four Chebyshev weights
Author(s) -
Davorka R. Jandrlić,
Aleksandar V. Pejčev,
Miodrag M. Spalević
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2203961j
Subject(s) - mathematics , quadrature (astronomy) , clenshaw–curtis quadrature , ellipse , chebyshev filter , gauss , mathematical analysis , gauss–kronrod quadrature formula , gaussian quadrature , numerical integration , chebyshev polynomials , nyström method , integral equation , geometry , physics , engineering , quantum mechanics , electrical engineering
In this paper, we consider the Kronrod extension for the Gauss-Radau and Gauss-Lobatto quadrature consisting of any one of the four Chebyshev weights. The main purpose is to effectively estimate the error of these quadrature formulas. This estimate needs a calculation of the maximum of the modulus of the kernel. We compute explicitly the kernel function and determine the locations on the ellipses where a maximum modulus of the kernel is attained. Based on this, we derive effective error bounds of the Kronrod extensions if the integrand is an analytic function inside of a region bounded by a confocal ellipse that contains the interval of integration.