A sinc-Hunter quadrature rule for Cauchy principal value integrals. (English) Zbl 0709.65115
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 \([-1,+1]\). An application of the rule to the approximate solution of Cauchy singular integral equations is discussed. Numerical examples are included to show the performance of the rule.
Reviewer: Yongsheng Sun
MSC:
| 65R20 | Numerical methods for integral equations |
| 65D32 | Numerical quadrature and cubature formulas |
| 30E20 | Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane |
| 41A55 | Approximate quadratures |
| 30E10 | Approximation in the complex plane |
| 45E05 | Integral equations with kernels of Cauchy type |
