Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 571583, 21 pages
Research Article

An Algorithm for the Numerical Evaluation of Certain Finite Part Integrals

1Department of Mathematics, Faculty of Sciences, Cairo University, Giza, Egypt
2Department of Mathematics, Faculty of Education, King Abdulaziz University, Jeddah 2356, Saudi Arabia
3Department of Mathematics, Faculty of Industrial Education, Helwan University, Cairo, Egypt
4Department of Mathematics, Faculty of Sciences, Shaqra University, Shaqra, Saudi Arabia

Received 14 March 2011; Accepted 19 April 2011

Academic Editor: Z. Huang

Copyright © 2011 Samir A. Ashour and Hany M. Ahmed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 ∫ βˆ— 𝑏 π‘Ž 𝑀 ( π‘₯ ) ( 𝑓 ( π‘₯ ) / ( π‘₯ βˆ’ 𝑑 ) π‘Ÿ ) 𝑑 π‘₯ , π‘Ÿ = 1 , 2 , … , and extend Clenshow's algorithm to evaluate these integrals in a stable way.