The extrapolation methods for computing Cauchy principal value integral on intervals

Abstract

The generalised composite rectangle (constant) rule for the computation of Cauchy principle value integral with kernel 1/(x – s) is discussed, and the asymptotic expansion of error function is obtained. Based on the asymptotic expansion, a series is constructed to approach the singular point. An extrapolation algorithm is presented and the convergence rate is proved. At last, some examples are also illustrated to confirm the theoretical results and show the efficiency of the algorithms.