NewtonCotes 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 5point rule. Explicit coefficients and error terms for higher orders are seldom given literature. Higherorder 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 19points 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 allround one.
Primary Language  en 

Subjects  Mathematics 
Journal Section  Articles 
Authors 

Dates 
Publication Date: August 30, 2019 
Bibtex  @research article { rna556971,
journal = {Results in Nonlinear Analysis},
issn = {},
eissn = {26367556},
address = {Erdal KARAPINAR},
year = {2019},
volume = {2},
pages = {48  60},
doi = {},
title = {A close look at NewtonCotes integration rules},
key = {cite},
author = {Sermutlu, Emre}
} 
APA  Sermutlu, E . (2019). A close look at NewtonCotes integration rules. Results in Nonlinear Analysis, 2 (2), 4860. Retrieved from http://dergipark.org.tr/rna/issue/45041/556971 
MLA  Sermutlu, E . "A close look at NewtonCotes integration rules". Results in Nonlinear Analysis 2 (2019): 4860 <http://dergipark.org.tr/rna/issue/45041/556971> 
Chicago  Sermutlu, E . "A close look at NewtonCotes integration rules". Results in Nonlinear Analysis 2 (2019): 4860 
RIS  TY  JOUR T1  A close look at NewtonCotes 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  26367556 M3  UR  Y2  2019 ER  
EndNote  %0 Results in Nonlinear Analysis A close look at NewtonCotes integration rules %A Emre Sermutlu %T A close look at NewtonCotes integration rules %D 2019 %J Results in Nonlinear Analysis %P 26367556 %V 2 %N 2 %R %U 
ISNAD  Sermutlu, Emre . "A close look at NewtonCotes integration rules". Results in Nonlinear Analysis 2 / 2 (August 2019): 4860. 
AMA  Sermutlu E . A close look at NewtonCotes integration rules. RNA. 2019; 2(2): 4860. 
Vancouver  Sermutlu E . A close look at NewtonCotes integration rules. Results in Nonlinear Analysis. 2019; 2(2): 6048. 