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.

Keywords:

• Cauchy principal value integral
• extrapolation method
• composite rectangle rule

Additional information

Notes on contributors

J Li

Jin Li received his MS degree in Computational Mathematics from the School of Sciences of Yanshan University, China, in 2007, and PhD degree in Computational Mathematics from the Chinese Academy of Science, China, in 2010. He joined the School of Science, Shandong Jianzhu University, China, in 2010, where he is currently an associate professor. His main research interests include boundary element methods and numerical mathematics for PDE.