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## A close look at Newton-Cotes integration rules

#### Emre Sermutlu [1]

##### 18 38

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.

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Primary Language en Mathematics Articles Orcid: 0000-0002-5151-0460Author: Emre Sermutlu (Primary Author)Institution: CANKAYA UNIVERSITYCountry: Turkey Publication Date: August 30, 2019
 Bibtex @research article { rna556971, journal = {Results in Nonlinear Analysis}, issn = {}, eissn = {2636-7556}, address = {Erdal KARAPINAR}, year = {2019}, volume = {2}, pages = {48 - 60}, doi = {}, title = {A close look at Newton-Cotes integration rules}, key = {cite}, author = {Sermutlu, Emre} } APA Sermutlu, E . (2019). A close look at Newton-Cotes integration rules. Results in Nonlinear Analysis, 2 (2), 48-60. Retrieved from http://dergipark.org.tr/rna/issue/45041/556971 MLA Sermutlu, E . "A close look at Newton-Cotes integration rules". Results in Nonlinear Analysis 2 (2019): 48-60 Chicago Sermutlu, E . "A close look at Newton-Cotes integration rules". Results in Nonlinear Analysis 2 (2019): 48-60 RIS TY - JOUR T1 - A close look at Newton-Cotes integration rules AU - Emre Sermutlu Y1 - 2019 PY - 2019 N1 - DO - T2 - Results in Nonlinear Analysis JF - Journal JO - JOR SP - 48 EP - 60 VL - 2 IS - 2 SN - -2636-7556 M3 - UR - Y2 - 2019 ER - EndNote %0 Results in Nonlinear Analysis A close look at Newton-Cotes integration rules %A Emre Sermutlu %T A close look at Newton-Cotes integration rules %D 2019 %J Results in Nonlinear Analysis %P -2636-7556 %V 2 %N 2 %R %U ISNAD Sermutlu, Emre . "A close look at Newton-Cotes integration rules". Results in Nonlinear Analysis 2 / 2 (August 2019): 48-60. AMA Sermutlu E . A close look at Newton-Cotes integration rules. RNA. 2019; 2(2): 48-60. Vancouver Sermutlu E . A close look at Newton-Cotes integration rules. Results in Nonlinear Analysis. 2019; 2(2): 60-48.