Geodesic
The error estimates of Kronrod extension for Gauss-Radau and Gauss-Lobatto quadrature with the four Chebyshev weights
Filomat, Tome 36 (2022) no. 3, p. 961

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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
DOI : 10.2298/FIL2203961J
Classification : 65D32, 65D30, 41A55
Keywords: Gauss-Kronrod quadrature formulae, Remainder term for analytic function, Error bound 
Davorka Jandrlić; Aleksandar Pejčev; Miodrag Spalević. The error estimates of Kronrod extension for Gauss-Radau and Gauss-Lobatto quadrature with the four Chebyshev weights. Filomat, Tome 36 (2022) no. 3, p. 961 . doi: 10.2298/FIL2203961J
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     title = {The error estimates of {Kronrod} extension for {Gauss-Radau} and {Gauss-Lobatto} quadrature with the four {Chebyshev} weights},
     journal = {Filomat},
     pages = {961 },
     year = {2022},
     volume = {36},
     number = {3},
     doi = {10.2298/FIL2203961J},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2203961J/}
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