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Mathematics of Computation

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Numerical evaluation of Cauchy principal value integrals with singular integrands

Author: Philip Rabinowitz
Journal: Math. Comp. 55 (1990), 265-275
MSC: Primary 65D30
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

$\displaystyle \oint k(x)(f(x)/(x - \lambda ))\,dx,\quad - 1 < \lambda < 1,$

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