The Error Estimates of Kronrod Extension for Gauss-Radau and Gauss-Lobatto Quadrature with the Four Chebyshev Weights
Апстракт
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.
Кључне речи:
Remainder term for analytic function / Gauss-Kronrod quadrature formulae / Error boundИзвор:
Filomat, 2022, 36, 3, 961-977Издавач:
- Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
Финансирање / пројекти:
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200105 (Универзитет у Београду, Машински факултет) (RS-MESTD-inst-2020-200105)
- Методе нумеричке и нелинеарне анализе са применама (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.2298/FIL2203961J
ISSN: 0354-5180
WoS: 000778010200021
Scopus: 2-s2.0-85130725366
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Jandrlić, Davorka AU - Pejčev, Aleksandar AU - Spalević, Miodrag PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3782 AB - 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. PB - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš T2 - Filomat T1 - The Error Estimates of Kronrod Extension for Gauss-Radau and Gauss-Lobatto Quadrature with the Four Chebyshev Weights EP - 977 IS - 3 SP - 961 VL - 36 DO - 10.2298/FIL2203961J ER -
@article{ author = "Jandrlić, Davorka and Pejčev, Aleksandar and Spalević, Miodrag", year = "2022", abstract = "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.", publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš", journal = "Filomat", title = "The Error Estimates of Kronrod Extension for Gauss-Radau and Gauss-Lobatto Quadrature with the Four Chebyshev Weights", pages = "977-961", number = "3", volume = "36", doi = "10.2298/FIL2203961J" }
Jandrlić, D., Pejčev, A.,& Spalević, M.. (2022). The Error Estimates of Kronrod Extension for Gauss-Radau and Gauss-Lobatto Quadrature with the Four Chebyshev Weights. in Filomat Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 36(3), 961-977. https://doi.org/10.2298/FIL2203961J
Jandrlić D, Pejčev A, Spalević M. The Error Estimates of Kronrod Extension for Gauss-Radau and Gauss-Lobatto Quadrature with the Four Chebyshev Weights. in Filomat. 2022;36(3):961-977. doi:10.2298/FIL2203961J .
Jandrlić, Davorka, Pejčev, Aleksandar, Spalević, Miodrag, "The Error Estimates of Kronrod Extension for Gauss-Radau and Gauss-Lobatto Quadrature with the Four Chebyshev Weights" in Filomat, 36, no. 3 (2022):961-977, https://doi.org/10.2298/FIL2203961J . .