Higher-Order Newton-Cotes Formulas
Abstract
Problem statement: The present work offers equations of Newton-Cotes Integration until twenty segments. Approach: It shows Newton-Cotes closed and open integration formulas. The new type Newton-Cotes semi-closed or semi-open was proposed. Results: An analysis of error in the technique was made. To estimate the error of integration in discrete data, we propose apply different rules or mix several rules. Conclusion/Recommendations: The difference in the result of each formula provides an approximation of the error. Computational routines to generate Newton-Cotes integration rules were presented.
DOI: https://doi.org/10.3844/jmssp.2010.193.204
Copyright: © 2010 Pedro Americo Almeida Magalhaes Junior and Cristina Almeida Magalhaes. This is an open access article distributed under the terms of the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
- Numerical methods
- numerical integration
- quadrature
- Newton-cotes
- higher-order
- analysis of error