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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Numerical evaluation of Cauchy principal value integrals with singular integrands


Author: Philip Rabinowitz
Journal: Math. Comp. 55 (1990), 265-275
MSC: Primary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1990-1023768-4
MathSciNet review: 1023768
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Abstract: Convergence results are proved for sequences of interpolatory integration rules for Cauchy principal value integrals of the form \[ \oint k(x)(f(x)/(x - \lambda )) dx,\quad - 1 < \lambda < 1,\] when $f(x)$ is singular at a point $\xi \ne \lambda$ and the singularity is ignored or avoided.


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Keywords: Cauchy principal value integrals, interpolatory integration rules, product integration rules, singular integrands, generalized smooth Jacobi weight
Article copyright: © Copyright 1990 American Mathematical Society