TY  - EJOU
AU  - Li, Jin 
AU  - Yu, De-hao 

TI  - Error Expansion of Classical Trapezoidal Rule for Computing Cauchy Principal Value Integral
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2013
VL  - 93
IS  - 1
SN  - 1526-1506

AB  - The composite classical trapezoidal rule for the computation of Cauchy principal value integral with the singular kernel 1/(x-s) is discussed. Based on the investigation of the superconvergence phenomenon, i.e., when the singular point coincides with some priori known point, the convergence rate of the classical trapezoidal rule is higher than the globally one which is the same as the Riemann integral for classical trapezoidal rule. The superconvergence phenomenon of the composite classical trapezoidal rule occurs at certain local coordinate of each subinterval and the corresponding superconvergence error estimate is obtained. Some numerical examples are provided to validate the theoretical analysis.
KW  - Cauchy principal value integral
KW  -  classical trapezoidal rule
KW  -  error expansion
KW  -  superconvergence

DO  - 10.3970/cmes.2013.093.047