Numerical evaluation of Cauchy principal value integrals with singular integrands

Rabinowitz, Philip

doi:10.1090/S0025-5718-1990-1023768-4

Numerical evaluation of Cauchy principal value integrals with singular integrands
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Math. Comp. 55 (1990), 265-275 Request permission

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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Some practical aspects in the numerical evaluation of Cauchy principal value integrals

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