Hadamard-Finite-Part simultaneous infrared and ultraviolet self-regularization of Universal functions in electrostatic limit

2015 ◽  
Author(s):  
Alireza Baghai-Wadji
Keyword(s):  
Finite Part ◽  
Universal Functions ◽  
Hadamard Finite Part

The superconvergence of composite Newton–Cotes rules for Hadamard finite-part integral on a circle

Computing ◽  
2009 ◽  
Vol 85 (3) ◽  
pp. 219-244 ◽  
Author(s):  
Xiaoping Zhang ◽  
Jiming Wu ◽  
Dehao Yu
Keyword(s):  
Finite Part ◽  
Hadamard Finite Part

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.

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