Extrapolation Methods for Computing Hadamard Finite-Part Integral on Finite Intervals

Extrapolation Methods for Computing Hadamard Finite-Part Integral on Finite Intervals

Year:    2019

Author:    Jin Li, Hongxing Rui

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 2 : pp. 261–277

Abstract

In this paper, we present the composite rectangle rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel 1/(x−s)and we obtain the asymptotic expansion of error function of the middle rectangle rule. Based on the asymptotic expansion, two extrapolation algorithms are presented and their convergence rates are proved, which are the same as the Euler-Maclaurin expansions of classical middle rectangle rule approximations. At last, some numerical results are also illustrated to confirm the theoretical results and show the efficiency of the algorithms.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1802-m2017-0027

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 2 : pp. 261–277

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Hadamard finite-part integral Extrapolation method Composite rectangle rule Superconvergence Error functional.

Author Details

Jin Li

Hongxing Rui

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