A sinc-Hunter quadrature rule for Cauchy principal value integrals

Author:
Bernard Bialecki

Journal:
Math. Comp. **55** (1990), 665-681

MSC:
Primary 65D30

DOI:
https://doi.org/10.1090/S0025-5718-1990-1035926-3

MathSciNet review:
1035926

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Abstract: A Sinc function approach is used to derive a new Hunter type quadrature rule for the evaluation of Cauchy principal value integrals of certain analytic functions. Integration over a general arc in the complex plane is considered. Special treatment is given to integrals over the interval .

It is shown that the quadrature error is of order , where *N* is the number of nodes used, and where *c* is a positive constant which is independent of *N*. An application of the rule to the approximate solution of Cauchy singular integral equations is also discussed. Numerical examples are included to illustrate the performance of the rule.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1990-1035926-3

Keywords:
Gauss quadratures,
Cauchy singular integral equations

Article copyright:
© Copyright 1990
American Mathematical Society