Superconvergence of the Composite Rectangle Rule for Computing Hypersingular Integral on Interval

Superconvergence of the Composite Rectangle Rule for Computing Hypersingular Integral on Interval

Year:    2020

Author:    Yongling Cheng, Jin Li, Zongcheng Li, Yongling Cheng, Zongcheng Li

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 3 : pp. 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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2019-0089

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 3 : pp. 770–787

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Hypersingular integral middle rectangle rule asymptotic expansion superconvergence phenomenon.

Author Details

Yongling Cheng

Jin Li

Zongcheng Li

Yongling Cheng

Zongcheng Li

  1. Cubic spline quadrature rule to calculate supersingular integral on interval

    Li, Jin

    Sang, Yu

    Zhang, Xiaolei

    Computational and Applied Mathematics, Vol. 41 (2022), Iss. 7

    https://doi.org/10.1007/s40314-022-02008-9 [Citations: 0]