scholarly journals Gaussian quadrature formulae of the third kind for Cauchy principal value integrals: Basic properties and error estimates

1995 ◽  
Vol 65 (1-3) ◽  
pp. 97-114 ◽  
Author(s):  
Kai Diethelm
Keyword(s):  
Error Estimates ◽  
Gaussian Quadrature ◽  
Cauchy Principal ◽  
Cauchy Principal Value ◽  
Quadrature Formulae ◽  
Basic Properties ◽  
The Third ◽  
Cauchy Principal Value Integrals ◽  
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.

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