On the convergence of some quadrature rules for Cauchy principal-value and finite-part integrals

Computing ◽  
1983 ◽  
Vol 31 (2) ◽  
pp. 105-114 ◽  
Author(s):  
G. Tsamasphyros ◽  
P. S. Theocaris
Keyword(s):  
Quadrature Rules ◽  
Finite Part ◽  
Cauchy Principal ◽  
Cauchy Principal Value ◽  
Principal Value

scholarly journals An Algorithm for the Numerical Evaluation of Certain Finite Part Integrals

2011 ◽  
Vol 2011 ◽  
pp. 1-21
Author(s):  
Samir A. Ashour ◽  
Hany M. Ahmed
Keyword(s):  
Numerical Evaluation ◽  
Gaussian Quadrature ◽  
Quadrature Rules ◽  
Finite Part ◽  
Cauchy Principal ◽  
Cauchy Principal Value ◽  
Cauchy Principal Value Integrals ◽  
Principal Value

Many algorithms that have been proposed for the numerical evaluation of Cauchy principal value integrals are numerically unstable. In this work we present some formulae to evaluate the known Gaussian quadrature rules for finite part integrals , and extend Clenshow's algorithm to evaluate these integrals in a stable way.

scholarly journals Some Derivative-Free Quadrature Rules for Numerical Approximations of Cauchy Principal Value of Integrals

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Rabindranath Das ◽  
Manoj Kumar Hota ◽  
Manoranjan Bej
Keyword(s):  
Quadrature Rules ◽  
Numerical Approximations ◽  
Approximate Evaluation ◽  
Cauchy Principal ◽  
Cauchy Principal Value ◽  
Derivative Free ◽  
Principal Value

Some derivative-free six-point quadrature rules for approximate evaluation of Cauchy principal value of integrals have been constructed in this paper. Rules are numerically verified by suitable integrals, their degrees of precision have been determined, and their respective errors have been asymptotically estimated.

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