The superconvergence of the Newton-Cotes rule for Cauchy principal value integrals |
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| Authors: | Dongjie Liu Dehao Yu |
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| Institution: | a Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, PR Chinab Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, PR Chinac LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, CAS, 100190 Beijing, PR China |
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| Abstract: | We consider the general (composite) Newton-Cotes method for the computation of Cauchy principal value integrals and focus on its pointwise superconvergence phenomenon, which means that the rate of convergence of the Newton-Cotes quadrature rule is higher than what is globally possible when the singular point coincides with some a priori known point. The necessary and sufficient conditions satisfied by the superconvergence point are given. Moreover, the superconvergence estimate is obtained and the properties of the superconvergence points are investigated. Finally, some numerical examples are provided to validate the theoretical results. |
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| Keywords: | 65D30 65D32 65R20 |
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