TY - EJOU
AU - Xia, Maohui
AU - Li, Jin
TI - Extrapolation Method for Cauchy Principal Value Integral with Classical Rectangle Rule on Interval
T2 - Computer Modeling in Engineering \& Sciences
PY - 2018
VL - 115
IS - 3
SN - 1526-1506
AB - In this paper, the classical composite middle rectangle rule for the computation of Cauchy principal value integral (the singular kernel 1/(x-s)) is discussed. With the density function approximated only while the singular kernel is calculated analysis, then the error functional of asymptotic expansion is obtained. We construct a series to approach the singular point. An extrapolation algorithm is presented and the convergence rate of extrapolation algorithm is proved. At last, some numerical results are presented to confirm the theoretical results and show the efficiency of the algorithms.
KW - Cauchy principal value integral
KW - Extrapolation method
KW - Composite rectangle rule
KW - Superconvergence
KW - Error expansion
DO - 10.3970/cmes.2018.08053