Midpoint Derivative-Based Closed Newton-Cotes Quadrature
A novel family of numerical integration of closed Newton-Cotes quadrature rules is presented which uses the derivative value at the midpoint. It is proved that these kinds of quadrature rules obtain an increase of two orders of precision over the classical closed Newton-Cotes formula, and the error...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/492507 |
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| _version_ | 1832558789699567616 |
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| author | Weijing Zhao Hongxing Li |
| author_facet | Weijing Zhao Hongxing Li |
| author_sort | Weijing Zhao |
| collection | DOAJ |
| description | A novel family of numerical integration of closed Newton-Cotes quadrature rules is presented which uses the derivative value at the midpoint. It is proved that these kinds of quadrature rules obtain an increase of two orders of precision over the classical closed Newton-Cotes formula, and the error terms are given. The computational cost for these methods is analyzed from the numerical point of view, and it has shown that the proposed formulas are superior computationally to the same order closed Newton-Cotes formula when they reduce the error below the same level. Finally, some numerical examples show the numerical superiority of the proposed approach with respect to closed Newton-Cotes formulas. |
| format | Article |
| id | doaj-art-3d635d09404a4d05b4cb42bb71a324b6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3d635d09404a4d05b4cb42bb71a324b62025-02-03T01:31:34ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/492507492507Midpoint Derivative-Based Closed Newton-Cotes QuadratureWeijing Zhao0Hongxing Li1Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, ChinaFaculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, ChinaA novel family of numerical integration of closed Newton-Cotes quadrature rules is presented which uses the derivative value at the midpoint. It is proved that these kinds of quadrature rules obtain an increase of two orders of precision over the classical closed Newton-Cotes formula, and the error terms are given. The computational cost for these methods is analyzed from the numerical point of view, and it has shown that the proposed formulas are superior computationally to the same order closed Newton-Cotes formula when they reduce the error below the same level. Finally, some numerical examples show the numerical superiority of the proposed approach with respect to closed Newton-Cotes formulas.http://dx.doi.org/10.1155/2013/492507 |
| spellingShingle | Weijing Zhao Hongxing Li Midpoint Derivative-Based Closed Newton-Cotes Quadrature Abstract and Applied Analysis |
| title | Midpoint Derivative-Based Closed Newton-Cotes Quadrature |
| title_full | Midpoint Derivative-Based Closed Newton-Cotes Quadrature |
| title_fullStr | Midpoint Derivative-Based Closed Newton-Cotes Quadrature |
| title_full_unstemmed | Midpoint Derivative-Based Closed Newton-Cotes Quadrature |
| title_short | Midpoint Derivative-Based Closed Newton-Cotes Quadrature |
| title_sort | midpoint derivative based closed newton cotes quadrature |
| url | http://dx.doi.org/10.1155/2013/492507 |
| work_keys_str_mv | AT weijingzhao midpointderivativebasedclosednewtoncotesquadrature AT hongxingli midpointderivativebasedclosednewtoncotesquadrature |