TY - JOUR
T1 - Extrapolation Methods for Computing Hadamard Finite-Part Integral on Finite Intervals
AU - Li , Jin
AU - Rui , Hongxing
JO - Journal of Computational Mathematics
VL - 2
SP - 261
EP - 277
PY - 2018
DA - 2018/09
SN - 37
DO - http://doi.org/10.4208/jcm.1802-m2017-0027
UR - https://global-sci.org/intro/article_detail/jcm/12679.html
KW - Hadamard finite-part integral, Extrapolation method, Composite rectangle
rule, Superconvergence, Error functional.
AB - <p style="text-align: justify;">In this paper, we present the composite rectangle rule for the computation of Hadamard
finite-part integrals in boundary element methods with the hypersingular kernel 1/(x−s)<sup>2&nbsp;</sup>and we obtain the asymptotic expansion of error function of the middle rectangle rule.
Based on the asymptotic expansion, two extrapolation algorithms are presented and their
convergence rates are proved, which are the same as the Euler-Maclaurin expansions of
classical middle rectangle rule approximations. At last, some numerical results are also
illustrated to confirm the theoretical results and show the efficiency of the algorithms.</p>