TY - JOUR
T1 - The Cubic Spline Rule for the Hadamard Finite-Part Integral on an Interval
AU - Gendai Gu, Sheng An & Meiling Zhao
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 906
EP - 922
PY - 2019
DA - 2019/04
SN - 12
DO - http://doi.org/10.4208/nmtma.OA-2018-0060
UR - https://global-sci.org/intro/article_detail/nmtma/13136.html
KW - hypersingular integral, cubic spline rule, superconvergence.
AB - <p style="text-align: justify;">We propose a cubic spline rule for the calculation of the Hadamard finite-part
integral on an interval. The error estimate is presented in theory, and the superconvergence result of the cubic spline rule for Hadamard finite-part integral is derived. When
the singular point coincides with a prior known point, the convergence rate is one order
higher than what is globally possible. Numerical experiments are given to demonstrate
the efficiency of the theoretical analysis.</p>