Abstract and Applied Analysis

New Derivative Based Open Newton-Cotes Quadrature Rules

Fiza Zafar, Saira Saleem, and Clarence O. E. Burg

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Abstract

Some new families of open Newton-Cotes rules which involve the combinations of function values and the evaluation of derivative at uniformly spaced points of the interval are presented. The order of accuracy of these numerical formulas is higher than that of the classical open Newton-Cotes formulas. An extensive comparison of the computational cost, order of accuracy, error terms, coefficients of the error terms, observed order of accuracy, CPU usage time, and results obtained from these formulas is given. The comparisons show that we have been able to define some new open Newton-Cotes rules which are superior to classical open rules for less number of nodes and less computational cost with increased order of accuracy.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 109138, 16 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273210

Digital Object Identifier
doi:10.1155/2014/109138

Mathematical Reviews number (MathSciNet)
MR3178845

Zentralblatt MATH identifier
07021750

Citation

Zafar, Fiza; Saleem, Saira; Burg, Clarence O. E. New Derivative Based Open Newton-Cotes Quadrature Rules. Abstr. Appl. Anal. 2014 (2014), Article ID 109138, 16 pages. doi:10.1155/2014/109138. https://projecteuclid.org/euclid.aaa/1412273210


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