Asymptotic error expansions and splitting extrapolation algorithm for two classes of two-dimensional Cauchy principal-value integrals

2019 ◽  
Vol 357 ◽  
pp. 107-118
Author(s):  
Yanying Ma ◽  
Jin Huang
Keyword(s):  
Two Dimensional ◽  
Cauchy Principal ◽  
Cauchy Principal Value ◽  
Cauchy Principal Value Integrals ◽  
Extrapolation Algorithm ◽  
Asymptotic Error ◽  
Splitting Extrapolation ◽  
Principal Value ◽  
Asymptotic Error Expansions

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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