The Cubic Spline Rule for the Hadamard Finite-Part Integral on an Interval

The Cubic Spline Rule for the Hadamard Finite-Part Integral on an Interval

Year:    2019

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 906–922

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2018-0060

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 906–922

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    hypersingular integral cubic spline rule superconvergence.

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