TY - JOUR T1 - Nodal-Type Newton-Cotes Rules for Fractional Hypersingular Integrals 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.