On quadrature and cubature formulas for a class of multiple singular integrals

1997 ◽  
Vol 49 (12) ◽  
pp. 1891-1898
Author(s):  
V. V. Akimenko
Keyword(s):  
Singular Integrals ◽  
Cubature Formulas ◽  
Multiple Singular Integrals

scholarly journals Modified Gauss-Legendre, Lobatto and Radau cubature formulas for the numerical evaluation of 2-D singular integrals

1983 ◽  
Vol 6 (3) ◽  
pp. 567-587 ◽  
Author(s):  
P. S. Theocaris
Keyword(s):  
Numerical Evaluation ◽  
Singular Integrals ◽  
Numerical Technique ◽  
Logarithmic Singularity ◽  
Complete Analysis ◽  
Cauchy Type ◽  
Two Dimensional ◽  
One Dimensional ◽  
Cubature Formulas ◽  
Principal Value

A numerical technique, first reported in 1979 in refs.[1] and [2], for the numerical evaluation of two-dimensional Cauchy-type principal-value integrals, is extended in this paper to include several cubature formlas of the Radau and Lobatto types. For the construction of such a cubature formula the 2-D singular integral is considered as an iterated one, and the second-order pole involved in this integral analyzed into a pair of complex poles. Based on this procedure, the methods of numerical integration, valid for one-dimensional singular integrals, are extanded to the case of two-dimensional singular integrals. The cubature formulas of the Lobatto- and Radau-type are now formulated to include the cases where some of the desired abscissas may be chosen accordins to any appropriate criterion.Moreover, the theory developed is enlarged to include the case of a 2-D principal-value integral, containing a logarithmic singularity. The validity of the results is illustrated by considering certain numerical examples. Furthermore, a complete analysis of the convergence and the construction of error estimates is also presented.

Rough multiple singular integrals along hypersurfaces

2011 ◽  
Vol 31 (5) ◽  
pp. 2081-2098
Author(s):  
Deng Liurui ◽  
Li Zhongkai ◽  
Ma Bolin ◽  
Wu Huoxiong
Keyword(s):  
Singular Integrals ◽  
Multiple Singular Integrals

scholarly journals New Recursive Representations for the Favard Constants with Application to Multiple Singular Integrals and Summation of Series

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Snezhana Georgieva Gocheva-Ilieva ◽  
Ivan Hristov Feschiev
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Singular Integrals ◽  
Integral Form ◽  
Summation Of Series ◽  
Recursion Formulas ◽  
Multiple Singular Integrals

There are obtained integral form and recurrence representations for some Fourier series and connected with them Favard constants. The method is based on preliminary integration of Fourier series which permits to establish general recursion formulas for Favard constants. This gives the opportunity for effective summation of infinite series and calculation of some classes of multiple singular integrals by the Favard constants.

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