Abstract

In this study, we comment about a wrong proof, at least incomplete, of the closed Newton Cotes error formulas for integration in a closed interval [a,b]. These error formulas appear as an intuitive generalization of the simple proof for the error formula of the trapezoidal rule, and their proofs present one controversial step, which converts the proofs in mischievous, or at least, this step needs a clear clarification that it is not easy to derive. The correct proof of such formulas comes from a technique based on the Peano kernel.

Details

Title
About a dubious proof of a correct result about closed Newton Cotes error formulas
Author
López, David J 1 ; Padilla, Jose A 1 ; Ruiz, Juan 1 ; Tapia, Carlos 1 ; Trillo, Juan C 1 

1  Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, Spain 
Publication year
2023
Publication date
2023
Publisher
De Gruyter Poland
e-ISSN
23915455
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1515/math-2023-0150
ProQuest document ID
2893031487
Copyright
© 2023. This work is published under http://creativecommons.org/licenses/by/4.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.