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Journal of Applied Mathematics
Volume 2013, Article ID 736834, 9 pages
Research Article

The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval

Jin Li1,2 and Xiuzhen Li1

1School of Science, Shandong Jianzhu University, Jinan 25010, China
2School of Mathematics, Shandong University, Jinan 250100, China

Received 3 August 2013; Revised 12 October 2013; Accepted 12 October 2013

Academic Editor: Kazutake Komori

Copyright © 2013 Jin Li and Xiuzhen Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The modified trapezoidal rule for the computation of hypersingular integrals in boundary element methods is discussed. When the special function of the error functional equals zero, the convergence rate is one order higher than the general case. A new quadrature rule is presented and the asymptotic expansion of error function is obtained. Based on the error expansion, not only do we obtain a high order of accuracy, but also a posteriori error estimate is conveniently derived. Some numerical results are also reported to confirm the theoretical results and show the efficiency of the algorithms.