A new interpolatory type quadrature rule for weighted Cauchy principal value integrals
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SCOPUS
- Title
- A new interpolatory type quadrature rule for weighted Cauchy principal value integrals
- Authors
- Jang, BG; Lee, H; Roh, KH
- Date Issued
- 2008-07
- Publisher
- EUDOXUS PRESS, LLC
- Abstract
- This paper presents a new interpolatory type quadrature rule for approximating the weighted Cauchy principal value integrals integral(-1)(1)(1 - t(2))(lambda-1/2)f(t)/(t - c)dt where - 1/2 < lambda < 1. We prove that the rule has almost optimal stability property behaving in the form O(K log n + L), where K and L are constants depending only on c. Also, when f(t) possesses continuous derivatives up to order p >= 0 and the derivative f(P)(t) satisfies Holder continuity of order p, we obtain that the rule has the convergence rate of O((A + B log n + n(2v))n(-p-rho)), where v is as small as we like and A and B are constants depending on c.
- Keywords
- Cauchy principal value integral; quadrature rule; trigonometric interpolation; singular integral; interpolatory type; NUMERICAL EVALUATION; SINGULAR-INTEGRALS; CONVERGENCE
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/22915
- ISSN
- 1521-1398
- Article Type
- Article
- Citation
- JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, vol. 10, no. 3, page. 271 - 281, 2008-07
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