A close look at Newton-Cotes integration rules

Emre SERMUTLU

Article Details

A close look at Newton-Cotes integration rules

Authors:

Emre SERMUTLU

Publisher:

Erdal KARAPINAR

Main Topics:

Mathematics

Journal:

Results in Nonlinear Analysis 2019 Vol.2 Issue 2, pp.48-60

Document Type:

Article

Publication Date:

8/2019

Document Language:

English

Document ID (Org No.):

2000604867

Frequency:

Quarterly

eISSN:

2636-7556

Abstract:

 


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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Article Details

A close look at Newton-Cotes integration rules

Authors: Emre SERMUTLU

Publisher: Erdal KARAPINAR

Main Topics: Mathematics

Journal: Results in Nonlinear Analysis 2019 Vol.2 Issue 2, pp.48-60

Document Type: Article

Publication Date: 8/2019

Document Language: English

Document ID (Org No.): 2000604867

Frequency: Quarterly

eISSN: 2636-7556

Issues

Authors:

Emre SERMUTLU

Publisher:

Erdal KARAPINAR

Main Topics:

Mathematics

Journal:

Results in Nonlinear Analysis 2019 Vol.2 Issue 2, pp.48-60

Document Type:

Article

Publication Date:

8/2019

Document Language:

English

Document ID (Org No.):

2000604867

Frequency:

Quarterly

eISSN:

2636-7556