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The Rectangle Rule for Computing Cauchy Principal Value Integral on Circle
School of Science, Shandong Jianzhu University, Jinan, China
School of Mathematics, Shandong University, Jinan, China
School of Science, Shandong University of Technology, Zibo, China
School of Mathematics and Statistics Science, Ludong University, Yantai, China
- 1 School of Science, Shandong Jianzhu University, Jinan, China
- 2 School of Mathematics, Shandong University, Jinan, China
- 3 School of Science, Shandong University of Technology, Zibo, China
- 4 School of Mathematics and Statistics Science, Ludong University, Yantai, China
American Journal of Computational Mathematics·Volume 06 (2016)·Pages 98–107·Published 27 April 2016·DOI10.4236/ajcm.2016.62011
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Abstract
The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel is discussed. We show that the superconvergence rate of the composite midpoint rule occurs at certain local coodinate of each subinterval and obtain the corresponding superconvergence error estimate. Then collation methods are presented to solve certain kind of Hilbert singular integral equation. At last, some numerical examples are provided to validate the theoretical analysis.
KeywordsCauchy Principal Value IntegralExtrapolation MethodComposite Rectangle RuleSuperconvergenceError Expansion
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