Year: 2018
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.270418.190818
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 697–714
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Hypersingular integrals fractional order nodal-type Newton-Cotes rules superconvergence.