Quadrature formulas for calculating integrals of piecewise continuous functions

DOI: https://doi.org/10.26565/2221-5646-2013-1061-03
Keywords: quadrature formulas, the speed of convergence, the polynomials of Chebyshev

Abstract

The interpolation quadrature formula for calculation of the integral of a function containing irreparable rupture of the rst kind had been obtained. This formula is exact for polynomials, the degree of which less than the number of interpolation points. The convergence of approximate values of integrals of the exact values of integrals had been shown. The estimates of the convergence rates had been given.

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References

Gandel'. Yu.V. Boundary-Value Problems for the Helmholtz Equation and their Discrete Mathematical Models // Journal of Mathematical Sciences. - 2010. - Vol. 171, 1. - Springer Science+Business Media, Inc. - P. 74-88.

Гандель Ю.В., Душкин В.Д. Математические модели двумерных задач дифракции: Сингулярные интегральные уравнения и численные методы дискретных особенностей: монография / Ю. В. Гандель, В. Д. Душкин. - Харьков. Акад. ВВ МВД Украины, 2012. - 544 с.

Lifanov I.K. Singular Integral Equations and Discrete Vortices/ I.K. Lifanov. - Utrecht, the Netherlands; Tokyo, Japan: VSP, 1996, - 475 p.

Ильинский А.С Колебания и волны в электродинамических системах с потерями / А.С. Ильинский , Г.Я. Слепян. - М. : Изд-во МГУ, 1983. - 231 с.

Кравченко В.Ф. Электродинамика сверхпроводящих структур. Теория, алгоритмы и методы вычислений / В.Ф. Кравченко. - М: ФИЗМАТЛИТ, 2006. - 280 с.

Гандель Ю.В. Лекции о численных методах для сингулярных интегральных уравнений. Введение в методы вычисления сингулярных и гиперсингулярных интегралов / Ю. В. Гандель. - Харьков: Изд-во Харьковского национального университета, 2001. - 92 с.

Published
2013-05-31
Cited
How to Cite
Dushkin, V. D. (2013). Quadrature formulas for calculating integrals of piecewise continuous functions. Visnyk of V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics, (1061), 30-36. https://doi.org/10.26565/2221-5646-2013-1061-03
Issue
No. 1061 (2013)
Section
Статті

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