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 - <p style="text-align: justify;">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.</p>