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2023•International Journal of Mathematical Engineering and Management SciencesOpen access

A Class of Quadrature Rules for Complex Cauchy Principal Value Integrals

Arup Kumar Saha, Manoj Kumar Hota, Prasant Mohanty

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Abstract

This article is fully devoted to the numerical approximation of Cauchy-type integrals in the complex plane. A class of degree eight quadrature rules is formulated from a family of Gauss-type two-point rules based on the method of extrapolation. The basic rules are developed and then composite rules are constructed from the basic rules. The Error bounds for each rule are determined. The validity of the method has been demonstrated by the provision of numerical experiments and their results.

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What this paper is about

This article is fully devoted to the numerical approximation of Cauchy-type integrals in the complex plane. A class of degree eight quadrature rules is formulated from a family of Gauss-type two-point rules based on the method of extrapolation. The basic rules are developed and then composite rules are constructed from the basic rules. The Error bounds for each rule are determined. The validity of the method has been demonstrated by the provision of numerical experiments and their results.

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Available abstract

This article is fully devoted to the numerical approximation of Cauchy-type integrals in the complex plane. A class of degree eight quadrature rules is formulated from a family of Gauss-type two-point rules based on the method of extrapolation. The basic rules are developed and then composite rules are constructed from the basic rules. The Error bounds for each rule are determined. The validity of the method has been demonstrated by the provision of numerical experiments and their results.

Key concepts: Gauss–Kronrod quadrature formula, Cauchy principal value, Gauss–Jacobi quadrature, Clenshaw–Curtis quadrature, Tanh-sinh quadrature, Mathematics, Extrapolation, Gaussian quadrature

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