The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval
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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/736834 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832564235181228032 |
|---|---|
| author | Jin Li Xiuzhen Li |
| author_facet | Jin Li Xiuzhen Li |
| author_sort | Jin Li |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fb429b586bdc4b5797cbf677ffcf2aa9 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-fb429b586bdc4b5797cbf677ffcf2aa92025-02-03T01:11:33ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/736834736834The Modified Trapezoidal Rule for Computing Hypersingular Integral on IntervalJin Li0Xiuzhen Li1School of Science, Shandong Jianzhu University, Jinan 25010, ChinaSchool of Science, Shandong Jianzhu University, Jinan 25010, ChinaThe 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.http://dx.doi.org/10.1155/2013/736834 |
| spellingShingle | Jin Li Xiuzhen Li The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval Journal of Applied Mathematics |
| title | The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval |
| title_full | The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval |
| title_fullStr | The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval |
| title_full_unstemmed | The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval |
| title_short | The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval |
| title_sort | modified trapezoidal rule for computing hypersingular integral on interval |
| url | http://dx.doi.org/10.1155/2013/736834 |
| work_keys_str_mv | AT jinli themodifiedtrapezoidalruleforcomputinghypersingularintegraloninterval AT xiuzhenli themodifiedtrapezoidalruleforcomputinghypersingularintegraloninterval AT jinli modifiedtrapezoidalruleforcomputinghypersingularintegraloninterval AT xiuzhenli modifiedtrapezoidalruleforcomputinghypersingularintegraloninterval |