Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 906-922.
Published online: 2019-04
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We propose a cubic spline rule for the calculation of the Hadamard finite-part integral on an interval. The error estimate is presented in theory, and the superconvergence result of the cubic spline rule for Hadamard finite-part integral is derived. When the singular point coincides with a prior known point, the convergence rate is one order higher than what is globally possible. Numerical experiments are given to demonstrate the efficiency of the theoretical analysis.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0060}, url = {http://global-sci.org/intro/article_detail/nmtma/13136.html} }We propose a cubic spline rule for the calculation of the Hadamard finite-part integral on an interval. The error estimate is presented in theory, and the superconvergence result of the cubic spline rule for Hadamard finite-part integral is derived. When the singular point coincides with a prior known point, the convergence rate is one order higher than what is globally possible. Numerical experiments are given to demonstrate the efficiency of the theoretical analysis.