Superconvergence and ultraconvergence of Newton-Cotes rules for supersingular integrals |
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Authors: | Jin Li Dehao Yu |
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Affiliation: | a LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, CAS, Beijing 100190, PR China b School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China |
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Abstract: | In this article, the general (composite) Newton-Cotes rules for evaluating Hadamard finite-part integrals with third-order singularity (which is also called “supersingular integrals”) are investigated and the emphasis is placed on their pointwise superconvergence and ultraconvergence. The main error of the general Newton-Cotes rules is derived, which is shown to be determined by a certain function . Based on the error expansion, the corresponding modified quadrature rules are also proposed. At last, some numerical experiments are carried out to validate the theoretical analysis. |
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Keywords: | 65D32 65D30 |
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