TY - JOUR
T1 - Superconvergence of the Composite Rectangle Rule for Computing Hypersingular Integral on Interval
AU - Li , Jin
AU - Cheng , Yongling
AU - Li , Zongcheng
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 770
EP - 787
PY - 2020
DA - 2020/03
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0089
UR - https://global-sci.org/intro/article_detail/nmtma/15784.html
KW - Hypersingular  integral, middle rectangle rule, asymptotic expansion,  superconvergence phenomenon.
AB - <p style="text-align: justify;">The generalized middle rectangle rule for the computation of certain hypersingular integrals is discussed. A generalized middle rectangle rule with the density function approximated and the singular kernel analysis calculated is presented and the asymptotic expansion of error functional is obtained. When the special function in the error functional equals to zero, the superconvergence point is obtained and the superconvergence phenomenon which is one order higher than the general case is presented. At last, numerical examples are given to confirm the theoretical results.</p>