Error expansion of classical mid-point rectangle rule for computing Cauchy principal value integrals on an interval
Error expansion of classical mid-point rectangle rule for computing Cauchy principal value integrals on an interval
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DOI：
10.1080/00207160.2013.873123
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发表时间：
2014-01
影响因子：
1.8
通讯作者：
Jin Li;Ju'e Yang;Dehao Yu
中科院分区：
文献类型：
--
作者：
Jin Li;Ju'e Yang;Dehao Yu
讨论了计算柯西主值积分的经典复合中点矩形法则。当奇点与某个先验已知点重合时，中点矩形法则的收敛速度比整体收敛速度快，这与Riemann积分的收敛速度相同，称为超收敛现象。证明了复合中矩形准则在每个子区间的局部坐标处的超收敛现象，并给出了相应的超收敛误差估计。最后通过数值算例验证了理论分析的正确性。
The classical composite mid-point rectangle rule for the computation of Cauchy principal value integrals is discussed. When the singular point coincides with some priori known point, the convergence rate of the mid-point rectangle rule is higher than the globally one the same as the Riemann integral which is called as superconvergence phenomenon. The superconvergence phenomenon of the composite mid-rectangle rule occurs at certain local coordinate of each subinterval and the corresponding superconvergence error estimate is obtained. At last,some numerical examples are provided to validate the theoretical analysis.