Volume 12, Issue 3
The Cubic Spline Rule for the Hadamard Finite-Part Integral on an Interval

Gendai Gu ,  Sheng An and Meiling Zhao

10.4208/nmtma.OA-2018-0060

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 906-922.

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  • Abstract

We propose a cubic spline rule for the calculation of the Hadamard finite-part integral on an interval. The error estimate is presented in theory, and the superconvergence result of the cubic spline rule for Hadamard finite-part integral is derived. When the singular point coincides with a prior known point, the convergence rate is one order higher than what is globally possible. Numerical experiments are given to demonstrate the efficiency of the theoretical analysis.

  • History

Published online: 2019-04

  • AMS Subject Headings

65M10, 78A48

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