@Article{EAJAM-8-697, author = {}, 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} }