Numerical evaluation of Cauchy principal value integrals with singular integrands. (English) Zbl 0708.65023
Convergence results are proved for sequences of interpolatory product integration rules for evaluating Cauchy principal value integrals over a finite interval, where the integrand (apart from the Cauchy denominator), can be regarded as a product of two functions k and f, the second of which is approximated by interpolation to construct integration rules. However, in the present case f is allowed to be singular at some point other than the Cauchy singularity, and the singularity is either ignored or avoided in the evaluations.
The paper is concerned primarily with Gauss, Lobatto or Radau type points derived from orthogonal polynomials. The generalized smooth Jacobi case is discussed in detail.
The paper is concerned primarily with Gauss, Lobatto or Radau type points derived from orthogonal polynomials. The generalized smooth Jacobi case is discussed in detail.
Reviewer: W.E.Smith
MSC:
| 65D32 | Numerical quadrature and cubature formulas |
| 41A55 | Approximate quadratures |
| 30E20 | Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane |
Keywords:
singular integrands; Gauss quadrature; Lobatto quadrature; Radau quadrature; Convergence; interpolatory product integration rules; Cauchy principal value integrals; Cauchy singularity; orthogonal polynomialsReferences:
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