TITLE:
The Rectangle Rule for Computing Cauchy Principal Value Integral on Circle
AUTHORS:
Jin Li, Benxue Gong, Wei Liu
KEYWORDS:
Cauchy Principal Value Integral, Extrapolation Method, Composite Rectangle Rule, Superconvergence, Error Expansion
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.6 No.2,
June
13,
2016
ABSTRACT: The
classical composite rectangle (constant) rule for the computation of Cauchy
principle value integral with the singular kernel is discussed. We show
that the superconvergence rate of the composite midpoint rule occurs at certain
local coodinate of each subinterval and obtain the corresponding
superconvergence error estimate. Then collation methods are presented to solve
certain kind of Hilbert singular integral equation. At last, some numerical
examples are provided to validate the theoretical analysis.