An Algorithm for the Numerical Evaluation of Certain Finite Part Integrals | Zendy

Samir A. Ashour | Zendy; Hany M. Ahmed | Zendy

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An Algorithm for the Numerical Evaluation of Certain Finite Part Integrals

Author(s) -

Samir A. Ashour,

Hany M. Ahmed

Publication year - 2011

Publication title -

isrn applied mathematics

Language(s) - English

Resource type - Journals

eISSN - 2090-5572

pISSN - 2090-5564

DOI - 10.5402/2011/571583

Subject(s) - cauchy principal value , mathematics , slater integrals , gaussian quadrature , quadrature (astronomy) , cauchy distribution , numerical integration , order of integration (calculus) , algorithm , gaussian , calculus (dental) , mathematical analysis , nyström method , integral equation , boundary value problem , physics , medicine , optics , dentistry , quantum mechanics , cauchy boundary condition , free boundary problem

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 ∫∗()(()/(−)), =1,2,…, and extend Clenshow's algorithm to evaluate these integrals in a stable way.

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