Volume 37, Issue 2
Extrapolation Methods for Computing Hadamard Finite-Part Integral on Finite Intervals

J. Comp. Math., 37 (2019), pp. 261-277.

Published online: 2018-09

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• 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.

65N30.

lijin@lsec.cc.ac.cn (Jin Li)

hxrui@sdu.edu.cn (Hongxing Rui)

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@Article{JCM-37-261, author = {Li , Jin and Rui , Hongxing}, title = {Extrapolation Methods for Computing Hadamard Finite-Part Integral on Finite Intervals}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {2}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1802-m2017-0027}, url = {http://global-sci.org/intro/article_detail/jcm/12679.html} }
TY - JOUR T1 - Extrapolation Methods for Computing Hadamard Finite-Part Integral on Finite Intervals AU - Li , Jin AU - Rui , Hongxing JO - Journal of Computational Mathematics VL - 2 SP - 261 EP - 277 PY - 2018 DA - 2018/09 SN - 37 DO - http://doi.org/10.4208/jcm.1802-m2017-0027 UR - https://global-sci.org/intro/article_detail/jcm/12679.html KW - Hadamard finite-part integral, Extrapolation method, Composite rectangle rule, Superconvergence, Error functional. AB -

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.

Jin Li & Hongxing Rui. (2019). Extrapolation Methods for Computing Hadamard Finite-Part Integral on Finite Intervals. Journal of Computational Mathematics. 37 (2). 261-277. doi:10.4208/jcm.1802-m2017-0027
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