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

    Maohui Xia1, Jin Li*,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.115, No.3, pp. 313-326, 2018, DOI: 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. More >

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