Open Access

ARTICLE

Extrapolation Method for Cauchy Principal Value Integral with Classical Rectangle Rule on Interval

Maohui Xia¹, Jin Li^*,2

1 School of Sciences, Yanshan University, Qinhuang Dao 066004, China.
2 School of Sciences, Shandong Jianzhu University, Jinan 250101, China.

* Corresponding Author: Jin Li. Email: .

Computer Modeling in Engineering & Sciences 2018, 115(3), 313-326. https://doi.org/10.3970/cmes.2018.08053

Abstract

In this paper, the classical composite middle rectangle rule for the computation of Cauchy principal value integral (the singular kernel 1/(x-s)) is discussed. With the density function approximated only while the singular kernel is calculated analysis, then the error functional of asymptotic expansion is obtained. We construct a series to approach the singular point. An extrapolation algorithm is presented and the convergence rate of extrapolation algorithm is proved. At last, some numerical results are presented to confirm the theoretical results and show the efficiency of the algorithms.

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Keywords

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