Error expansion of trapezoidal rule for certain two-dimensional Cauchy principal value integrals

In this article, we discuss the classical composite trapezoidal rule for the computation of two dimensional singular integrals. The purpose is to obtain the convergence results O(h2) which is the same as the Riemann integral convergence rate at certain points of the classical composite trapezoidal rule. With the error functional of trapezoidal rule for computing two dimensional singular integrals, we get the superconvergence phenomenon when the special function in error functional is equal to zero. At last, some numerical examples are reported to illustrate our theoretical analysis which agree with it very well.