Comments on the Nature of Automatic Quadrature Routines

1976 ◽  
Vol 2 (1) ◽  
pp. 65-81 ◽  
Author(s):  
J. N. Lyness ◽  
J. J. Kaganove
Keyword(s):  
Automatic Quadrature

AUTOMATIC QUADRATURE SCHEME FOR EVALUATING HYPERSINGULAR INTEGRALS

2012 ◽  
Vol 09 ◽  
pp. 581-585
Author(s):  
SUZAN J. OBAIYS ◽  
Z. K. ESKHUVATOV ◽  
N. M. A. NIK LONG
Keyword(s):  
Numerical Experiments ◽  
Second Order ◽  
Close Connection ◽  
Finite Part ◽  
Smooth Functions ◽  
Hypersingular Integrals ◽  
Quadrature Scheme ◽  
Hadamard Finite Part ◽  
Automatic Quadrature

Hasegawa constructed the automatic quadrature scheme (AQS), of Cauchy principle value integrals for smooth functions. There is a close connection between Hadamard and Cauchy principle value integral. In this paper, we modify AQS for hypersingular integrals with second-order singularities, using hasegawa's formula and based on the relations between Hadamard finite part integral and Cauchy principle value integral. Numerical experiments are also given, to validate the modified AQS.

scholarly journals Asymptotic Behavior of Automatic Quadrature

1994 ◽  
Vol 10 (3) ◽  
pp. 296-340 ◽  
Author(s):  
Paola Favati ◽  
Grazia Lotti ◽  
Gaspare Di Marco ◽  
Francesco Romani
Keyword(s):  
Asymptotic Behavior ◽  
Automatic Quadrature

Efficient automatic quadrature in 3-d Galerkin BEM

1998 ◽  
Vol 157 (3-4) ◽  
pp. 215-224 ◽  
Author(s):  
Stefan Erichsen ◽  
Stefan A. Sauter
Keyword(s):  
Automatic Quadrature

Automatic quadrature of functions of the formg(¦f(x¦)

1996 ◽  
Vol 36 (2) ◽  
pp. 387-394 ◽  
Author(s):  
Antoinetta Venter ◽  
Dirk P. Laurie
Keyword(s):  
Automatic Quadrature

Error estimation in automatic quadrature routines

1991 ◽  
Vol 17 (2) ◽  
pp. 233-252 ◽  
Author(s):  
Jarle Berntsen ◽  
Terje O. Espelid
Keyword(s):  
Error Estimation ◽  
Automatic Quadrature

scholarly journals Generalized Chebyshev interpolation and its application to automatic quadrature

1983 ◽  
Vol 41 (164) ◽  
pp. 537-537 ◽  
Author(s):  
Takemitsu Hasegawa ◽  
Tatsuo Torii ◽  
Ichizo Ninomiya
Keyword(s):  
Chebyshev Interpolation ◽  
Automatic Quadrature

scholarly journals Approximating Cauchy-type singular integral by an automatic quadrature scheme

2011 ◽  
Vol 235 (16) ◽  
pp. 4675-4686 ◽  
Author(s):  
Z.K. Eshkuvatov ◽  
A. Ahmedov ◽  
N.M.A. Nik Long ◽  
N.J. Amalina
Keyword(s):  
Singular Integral ◽  
Cauchy Type ◽  
Quadrature Scheme ◽  
Automatic Quadrature
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