The Trapezoidal Rule for Computing Cauchy Principal Value Integral on Circle
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-10-05
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
The composite trapezoidal rule for the computation of Cauchy principal value integral with the singular kernel cot ( ( x - s ) / 2 ) is discussed.
Our study is based on the investigation of the pointwise superconvergence phenomenon; that is, when the singular point coincides with some a priori known point, the convergence rate of the trapezoidal rule is higher than what is globally possible.
We show that the superconvergence rate of the composite trapezoidal rule occurs at middle of each subinterval and obtain the corresponding superconvergence error estimate.
Some numerical examples are provided to validate the theoretical analysis.
American Psychological Association (APA)
Li, Jin. 2015. The Trapezoidal Rule for Computing Cauchy Principal Value Integral on Circle. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1075052
Modern Language Association (MLA)
Li, Jin. The Trapezoidal Rule for Computing Cauchy Principal Value Integral on Circle. Mathematical Problems in Engineering No. 2015 (2015), pp.1-9.
https://search.emarefa.net/detail/BIM-1075052
American Medical Association (AMA)
Li, Jin. The Trapezoidal Rule for Computing Cauchy Principal Value Integral on Circle. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1075052
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1075052