Modified gauss-jacobi quadrature formulas for the numerical evaluation of cauchy type singular integrals

1974 ◽  
Vol 14 (1) ◽  
pp. 14-21 ◽  
Author(s):  
M. M. Chawla ◽  
T. R. Ramakrishnan
Keyword(s):  
Numerical Evaluation ◽  
Singular Integrals ◽  
Quadrature Formulas ◽  
Cauchy Type

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.

scholarly journals Numerical evaluation for Cauchy type singular integrals on the interval

2010 ◽  
Vol 233 (8) ◽  
pp. 1995-2001 ◽  
Author(s):  
Z.K. Eshkuvatov ◽  
N.M.A. Nik Long ◽  
M. Abdulkawi
Keyword(s):  
Numerical Evaluation ◽  
Singular Integrals ◽  
Cauchy Type

The numerical evaluation of singular integrals with coth-kernel

1987 ◽  
Vol 27 (3) ◽  
pp. 389-402 ◽  
Author(s):  
Walter Gautschi ◽  
M. A. Kovačević ◽  
Gradimir V. Milovanović
Keyword(s):  
Numerical Evaluation ◽  
Singular Integrals
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