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Volume 8, Issue 4
Nodal-Type Newton-Cotes Rules for Fractional Hypersingular Integrals

Yan Gao, Hui Feng, Hao Tian, Lili Ju & Xiaoping Zhang

DOI: 10.4208/eajam.270418.190818

East Asian J. Appl. Math., 8 (2018), pp. 697-714.

Published online: 2018-10

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  • Abstract

Nodal-type Newton-Cotes rules for fractional hypersingular integrals based on the piecewise k-th order Newton interpolations are proposed. A general error estimate is first derived on quasi-uniform meshes and then we show that the even-order rules exhibit the superconvergence phenomenon — i.e. if the singular point is far away from the endpoints then the accuracy of the method is one order higher than the general estimate. Numerical experiments confirm the theoretical results.

  • Keywords

Hypersingular integrals, fractional order, nodal-type Newton-Cotes rules, superconvergence.

  • AMS Subject Headings

65D30, 65D32, 45E99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-697, author = {Yan Gao, Hui Feng, Hao Tian, Lili Ju and Xiaoping Zhang}, title = {Nodal-Type Newton-Cotes Rules for Fractional Hypersingular Integrals}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {4}, pages = {697--714}, abstract = {

Nodal-type Newton-Cotes rules for fractional hypersingular integrals based on the piecewise k-th order Newton interpolations are proposed. A general error estimate is first derived on quasi-uniform meshes and then we show that the even-order rules exhibit the superconvergence phenomenon — i.e. if the singular point is far away from the endpoints then the accuracy of the method is one order higher than the general estimate. Numerical experiments confirm the theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.270418.190818 }, url = {http://global-sci.org/intro/article_detail/eajam/12815.html} }
TY - JOUR T1 - Nodal-Type Newton-Cotes Rules for Fractional Hypersingular Integrals AU - Yan Gao, Hui Feng, Hao Tian, Lili Ju & Xiaoping Zhang JO - East Asian Journal on Applied Mathematics VL - 4 SP - 697 EP - 714 PY - 2018 DA - 2018/10 SN - 8 DO - http://doi.org/10.4208/eajam.270418.190818 UR - https://global-sci.org/intro/article_detail/eajam/12815.html KW - Hypersingular integrals, fractional order, nodal-type Newton-Cotes rules, superconvergence. AB -

Nodal-type Newton-Cotes rules for fractional hypersingular integrals based on the piecewise k-th order Newton interpolations are proposed. A general error estimate is first derived on quasi-uniform meshes and then we show that the even-order rules exhibit the superconvergence phenomenon — i.e. if the singular point is far away from the endpoints then the accuracy of the method is one order higher than the general estimate. Numerical experiments confirm the theoretical results.

Yan Gao, Hui Feng, Hao Tian, Lili Ju and Xiaoping Zhang. (2018). Nodal-Type Newton-Cotes Rules for Fractional Hypersingular Integrals. East Asian Journal on Applied Mathematics. 8 (4). 697-714. doi:10.4208/eajam.270418.190818
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