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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 2, Pages 86–92
DOI: https://doi.org/10.26907/0021-3446-2021-2-86-92 (Mi ivm9651) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Brief communications

Algorithm for construction of quadrature formulas with exponential convergence for linear operators acting on periodic functions

A. G. Petrov

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Ave. Vernadskogo, 101-1, Moscow, 119526 Russia
Full-text PDF (308 kB) Citations (4)
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DOI: https://doi.org/10.26907/0021-3446-2021-2-86-92
Abstract: The algorithm of the derivation of quadrature formulas for the calculation of linear operators acting on periodic functions is presented. For analytic functions, the order of accuracy of quadrature formulas increases indefinitely with the number of grid nodal points increasing. With sufficiently general restrictions on the kernels of linear operators, an exponential valuation of the quadrature formula has been proved. As examples, the quadrature formulas for the calculation of integral operators with logarithmic singularities used in the boundary element method to derive superconvergent numerical schemes for solving boundary value problems of harmonic and biharmonic equations on the plane, have been obtained.
Keywords: quadrature formula, linear operator, periodic function, Fourier series, harmonic and biharmonic functions, boundary value problem.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation АААА-А20-120011690138-6
Received: 23.11.2020
Revised: 23.11.2020
Accepted: 24.12.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 2, Pages 75–80
DOI: https://doi.org/10.3103/S1066369X21020080
Bibliographic databases:
Document Type: Article
UDC: 519.632
Language: Russian
Citation: A. G. Petrov, “Algorithm for construction of quadrature formulas with exponential convergence for linear operators acting on periodic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 2, 86–92; Russian Math. (Iz. VUZ), 65:2 (2021), 75–80
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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