An Algorithm for the Numerical Evaluation of Certain Finite Part Integrals-Reference-Cited by-同舟云学术

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An Algorithm for the Numerical Evaluation of Certain Finite Part Integrals

Published:2011-06-22 Issue: Volume:2011 Page:1-21
ISSN:2090-5564
Container-title:ISRN Applied Mathematics
language:en
Short-container-title:ISRN Applied Mathematics

Author:

Ashour Samir A.¹²,Ahmed Hany M.³⁴^ORCID

Affiliation:

1. Department of Mathematics, Faculty of Sciences, Cairo University, Giza, Egypt

2. Department of Mathematics, Faculty of Education, King Abdulaziz University, Jeddah 2356, Saudi Arabia

3. Department of Mathematics, Faculty of Industrial Education, Helwan University, Cairo, Egypt

4. Department of Mathematics, Faculty of Sciences, Shaqra University, Shaqra, Saudi Arabia

Abstract

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.

Publisher

Hindawi Limited

Subject

General Medicine

Link

http://downloads.hindawi.com/archive/2011/571583.pdf

Reference17 articles.

1. Formule gaussiane per il calcolo di integrali a valor principale secondo Cauchy e loro convergenza

2. On the convergence of Hunter's quadrature rule for Cauchy principal value integrals

3. Gauss type quadrature rules for Cauchy principal value integrals

4. Some Gauss-type formulae for the evaluation of Cauchy principal values of integrals

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