Open Access

ARTICLE

Error Expansion of Classical Trapezoidal Rule for Computing Cauchy Principal Value Integral

Jin Li¹, De-hao Yu^{2, 3}

1 School of Sciences, Shandong Jianzhu University, Jinan 250101, China.
2 School of Mathematical Sciences, Xiamen University, Xiamen 361005, China.
3 LSEC, ICMSEC, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190 , China.

Computer Modeling in Engineering & Sciences 2013, 93(1), 47-67. https://doi.org/10.3970/cmes.2013.093.047

Abstract

The composite classical trapezoidal rule for the computation of Cauchy principal value integral with the singular kernel 1/(x-s) is discussed. Based on the investigation of the superconvergence phenomenon, i.e., when the singular point coincides with some priori known point, the convergence rate of the classical trapezoidal rule is higher than the globally one which is the same as the Riemann integral for classical trapezoidal rule. The superconvergence phenomenon of the composite classical trapezoidal rule occurs at certain local coordinate of each subinterval and the corresponding superconvergence error estimate is obtained. Some numerical examples are provided to validate the theoretical analysis.

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Keywords

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