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Volume 13, Issue 3
Superconvergence of the Composite Rectangle Rule for Computing Hypersingular Integral on Interval

Jin Li, Yongling Cheng & Zongcheng Li

DOI: 10.4208/nmtma.OA-2019-0089

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 770-787.

Published online: 2020-03

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  • Abstract

The generalized middle rectangle rule for the computation of certain hypersingular integrals is discussed. A generalized middle rectangle rule with the density function approximated and the singular kernel analysis calculated is presented and the asymptotic expansion of error functional is obtained. When the special function in the error functional equals to zero, the superconvergence point is obtained and the superconvergence phenomenon which is one order higher than the general case is presented. At last, numerical examples are given to confirm the theoretical results.

  • Keywords

Hypersingular integral, middle rectangle rule, asymptotic expansion, superconvergence phenomenon.

  • AMS Subject Headings

32A55, 40A10, 65D30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

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

chengzi 0905@sdjzu.edu.cn (Zongcheng Li)

  • BibTex
  • RIS
  • TXT
@Article{NMTMA-13-770, author = {Li , JinCheng , Yongling and Li , Zongcheng}, title = {Superconvergence of the Composite Rectangle Rule for Computing Hypersingular Integral on Interval}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {3}, pages = {770--787}, abstract = {

The generalized middle rectangle rule for the computation of certain hypersingular integrals is discussed. A generalized middle rectangle rule with the density function approximated and the singular kernel analysis calculated is presented and the asymptotic expansion of error functional is obtained. When the special function in the error functional equals to zero, the superconvergence point is obtained and the superconvergence phenomenon which is one order higher than the general case is presented. At last, numerical examples are given to confirm the theoretical results.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0089}, url = {http://global-sci.org/intro/article_detail/nmtma/15784.html} }
TY - JOUR T1 - Superconvergence of the Composite Rectangle Rule for Computing Hypersingular Integral on Interval AU - Li , Jin AU - Cheng , Yongling AU - Li , Zongcheng JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 770 EP - 787 PY - 2020 DA - 2020/03 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2019-0089 UR - https://global-sci.org/intro/article_detail/nmtma/15784.html KW - Hypersingular integral, middle rectangle rule, asymptotic expansion, superconvergence phenomenon. AB -

The generalized middle rectangle rule for the computation of certain hypersingular integrals is discussed. A generalized middle rectangle rule with the density function approximated and the singular kernel analysis calculated is presented and the asymptotic expansion of error functional is obtained. When the special function in the error functional equals to zero, the superconvergence point is obtained and the superconvergence phenomenon which is one order higher than the general case is presented. At last, numerical examples are given to confirm the theoretical results.

Li , JinCheng , Yongling and Li , Zongcheng. (2020). Superconvergence of the Composite Rectangle Rule for Computing Hypersingular Integral on Interval. Numerical Mathematics: Theory, Methods and Applications. 13 (3). 770-787. doi:10.4208/nmtma.OA-2019-0089
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