The Trapezoidal Rule for Computing Cauchy Principal Value Integral on Circle
The composite trapezoidal rule for the computation of Cauchy principal value integral with the singular kernel cot((x-s)/2) is discussed. Our study is based on the investigation of the pointwise superconvergence phenomenon; that is, when the singular point coincides with some a priori known point, t...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2015-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2015/918083 |
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doaj-1518f00b1cc8479e8fa61170ccf7f17f2020-11-25T00:24:57ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/918083918083The Trapezoidal Rule for Computing Cauchy Principal Value Integral on CircleJin Li0School of Science, Shandong Jianzhu University, Jinan 250101, ChinaThe composite trapezoidal rule for the computation of Cauchy principal value integral with the singular kernel cot((x-s)/2) is discussed. Our study is based on the investigation of the pointwise superconvergence phenomenon; that is, when the singular point coincides with some a priori known point, the convergence rate of the trapezoidal rule is higher than what is globally possible. We show that the superconvergence rate of the composite trapezoidal rule occurs at middle of each subinterval and obtain the corresponding superconvergence error estimate. Some numerical examples are provided to validate the theoretical analysis.http://dx.doi.org/10.1155/2015/918083 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jin Li |
| spellingShingle |
Jin Li The Trapezoidal Rule for Computing Cauchy Principal Value Integral on Circle Mathematical Problems in Engineering |
| author_facet |
Jin Li |
| author_sort |
Jin Li |
| title |
The Trapezoidal Rule for Computing Cauchy Principal Value Integral on Circle |
| title_short |
The Trapezoidal Rule for Computing Cauchy Principal Value Integral on Circle |
| title_full |
The Trapezoidal Rule for Computing Cauchy Principal Value Integral on Circle |
| title_fullStr |
The Trapezoidal Rule for Computing Cauchy Principal Value Integral on Circle |
| title_full_unstemmed |
The Trapezoidal Rule for Computing Cauchy Principal Value Integral on Circle |
| title_sort |
trapezoidal rule for computing cauchy principal value integral on circle |
| publisher |
Hindawi Limited |
| series |
Mathematical Problems in Engineering |
| issn |
1024-123X 1563-5147 |
| publishDate |
2015-01-01 |
| description |
The composite trapezoidal rule for the computation of Cauchy principal value integral with the singular kernel cot((x-s)/2) is discussed. Our study is based on the investigation of the pointwise superconvergence phenomenon; that is, when the singular point coincides with some a priori known point, the convergence rate of the trapezoidal rule is higher than what is globally possible. We show that the superconvergence rate of the composite trapezoidal rule occurs at middle of each subinterval and obtain the corresponding superconvergence error estimate. Some numerical examples are provided to validate the theoretical analysis. |
| url |
http://dx.doi.org/10.1155/2015/918083 |
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