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Volume 12, Issue 3
The Cubic Spline Rule for the Hadamard Finite-Part Integral on an Interval

Gendai Gu, Sheng An & Meiling Zhao

DOI: 10.4208/nmtma.OA-2018-0060

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 906-922.

Published online: 2019-04

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  • Abstract

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.

  • Keywords

hypersingular integral, cubic spline rule, superconvergence.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-12-906, author = {Gendai Gu, Sheng An and Meiling Zhao}, title = {The Cubic Spline Rule for the Hadamard Finite-Part Integral on an Interval}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2019}, volume = {12}, number = {3}, pages = {906--922}, abstract = {

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} }
TY - JOUR T1 - The Cubic Spline Rule for the Hadamard Finite-Part Integral on an Interval AU - Gendai Gu, Sheng An & Meiling Zhao JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 906 EP - 922 PY - 2019 DA - 2019/04 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0060 UR - https://global-sci.org/intro/article_detail/nmtma/13136.html KW - hypersingular integral, cubic spline rule, superconvergence. AB -

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.

Gendai Gu, Sheng An and Meiling Zhao. (2019). The Cubic Spline Rule for the Hadamard Finite-Part Integral on an Interval. Numerical Mathematics: Theory, Methods and Applications. 12 (3). 906-922. doi:10.4208/nmtma.OA-2018-0060
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