Superconvergence of the composite Simpson’s rule for a certain finite-part integral and its applications |
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| Authors: | Xiaoping Zhang Jiming Wu Dehao Yu |
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| Institution: | 1. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, CAS, Beijing 100080, PR China;2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, PR China |
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| Abstract: | The superconvergence phenomenon of the composite Simpson’s rule for the finite-part integral with a third-order singularity is studied. The superconvergence points are located and the superconvergence estimate is obtained. Some applications of the superconvergence result, including the evaluation of the finite-part integrals and the solution of a certain finite-part integral equation, are also discussed and two algorithms are suggested. Numerical experiments are presented to confirm the superconvergence analysis and to show the efficiency of the algorithms. |
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| Keywords: | 65D32 65D30 65R20 |
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