A close look at Newton–Cotes integration rules
Newton–Cotes integration rules are the simplest methods in numerical integration. The main advantage of using these rules in quadrature software is ease of programming. In practice, only the lower orders are implemented or tested, because of the negative coefficients of higher orders. Most textboo...
| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Erdal KARAPINAR
2019-05-01
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| Series: | Results in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/711121 |
| _version_ | 1797906078022762496 |
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| author | Emre Sermutlu |
| author_facet | Emre Sermutlu |
| author_sort | Emre Sermutlu |
| collection | DOAJ |
| description | Newton–Cotes integration rules are the simplest methods in numerical integration. The main advantage
of using these rules in quadrature software is ease of programming. In practice, only the lower orders are
implemented or tested, because of the negative coefficients of higher orders. Most textbooks state it is
not necessary to go beyond Boole’s 5-point rule. Explicit coefficients and error terms for higher orders are
seldom given literature. Higher-order rules include negative coefficients therefore roundoff error increases
while truncation error decreases as we increase the number of points. But is the optimal one really Simpson
or Boole?
In this paper, we list coefficients up to 19-points for both open and closed rules, derive the error terms using an elementary and intuitive method, and test the rules on a battery of functions to find the optimum all-round one. |
| first_indexed | 2024-04-10T10:15:21Z |
| format | Article |
| id | doaj.art-1e8c84c2352e4b0ba076d7d0b6cb8f17 |
| institution | Directory Open Access Journal |
| issn | 2636-7556 2636-7556 |
| language | English |
| last_indexed | 2024-04-10T10:15:21Z |
| publishDate | 2019-05-01 |
| publisher | Erdal KARAPINAR |
| record_format | Article |
| series | Results in Nonlinear Analysis |
| spelling | doaj.art-1e8c84c2352e4b0ba076d7d0b6cb8f172023-02-15T16:21:56ZengErdal KARAPINARResults in Nonlinear Analysis2636-75562636-75562019-05-01224860A close look at Newton–Cotes integration rulesEmre SermutluNewton–Cotes integration rules are the simplest methods in numerical integration. The main advantage of using these rules in quadrature software is ease of programming. In practice, only the lower orders are implemented or tested, because of the negative coefficients of higher orders. Most textbooks state it is not necessary to go beyond Boole’s 5-point rule. Explicit coefficients and error terms for higher orders are seldom given literature. Higher-order rules include negative coefficients therefore roundoff error increases while truncation error decreases as we increase the number of points. But is the optimal one really Simpson or Boole? In this paper, we list coefficients up to 19-points for both open and closed rules, derive the error terms using an elementary and intuitive method, and test the rules on a battery of functions to find the optimum all-round one.https://dergipark.org.tr/en/download/article-file/711121quadraturenewton–cotestruncation errormatlab |
| spellingShingle | Emre Sermutlu A close look at Newton–Cotes integration rules Results in Nonlinear Analysis quadrature newton–cotes truncation error matlab |
| title | A close look at Newton–Cotes integration rules |
| title_full | A close look at Newton–Cotes integration rules |
| title_fullStr | A close look at Newton–Cotes integration rules |
| title_full_unstemmed | A close look at Newton–Cotes integration rules |
| title_short | A close look at Newton–Cotes integration rules |
| title_sort | close look at newton cotes integration rules |
| topic | quadrature newton–cotes truncation error matlab |
| url | https://dergipark.org.tr/en/download/article-file/711121 |
| work_keys_str_mv | AT emresermutlu acloselookatnewtoncotesintegrationrules AT emresermutlu closelookatnewtoncotesintegrationrules |