The adaptive composite trapezoidal rule for Hadamard finite-part integrals on an interval

作者：Liu, Dongjie; Wu, Jiming; Zhang, Xiaoping^*

来源：Journal of Computational and Applied Mathematics, 2017, 325: 165-174.

DOI：10.1016/j.cam.2017.04.041

• Adaptivity
• Trapezoidal rule
• Hadamard finite-part integrals
• Error estimate

In this article, we discuss an adaptive strategy of implementing trapezoidal rule for evaluating Hadamard finite-part integrals with kernels having different singularity. The purpose is to demonstrate cost savings and fast convergence rates engendered through adaptivity for the computation of finite-part integrals. The error indicators obtained from the a posteriori error estimate are used for mesh refinement. Numerical experiments demonstrate that the a posteriori error estimate is efficient, and there is no reliability-efficient gap.

• 出版日期2017-12-1
• 单位武汉大学; 上海大学; 北京应用物理与计算数学研究所