Efficient numerical methods for Cauchy principal value integrals with highly oscillatory integrands

Xu, Zhenhua; Lv, Zhanmei; Geng, Hongrui

doi:10.1007/s11075-022-01302-1

Cited by 3 publications

(1 citation statement)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To enhance the accuracy of the numerical integration method through the coordinate transformation, he presented simple rational functions, including parameters. Xu et al (2022) evaluated a particular type of CPV integrals with oscillatory integrands by transforming two line integrals and then computing them using the Gauss quadrature rule. In their article, Saha et al (2022) formulated non-classical quadrature schemes for the approximation of Cauchy-type oscillatory and singular integrals in the complex plane.…”

Section: 𝑑𝑧mentioning

confidence: 99%

A Class of Quadrature Rules for Complex Cauchy Principal Value Integrals

Saha,

Hota,

Mohanty

2023

Int. j. math. eng. manag. sci.

View full text Add to dashboard Cite

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.

show abstract

Section: 𝑑𝑧mentioning

confidence: 99%