Research Article Open Access

Higher-Order Newton-Cotes Formulas

Pedro Americo Almeida Magalhaes Junior and Cristina Almeida Magalhaes

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.

Journal of Mathematics and Statistics
Volume 6 No. 2, 2010, 193-204

DOI: https://doi.org/10.3844/jmssp.2010.193.204

Submitted On: 25 March 2010 Published On: 30 June 2010

How to Cite: Junior, P. A. A. M. & Magalhaes, C. A. (2010). Higher-Order Newton-Cotes Formulas. Journal of Mathematics and Statistics, 6(2), 193-204. https://doi.org/10.3844/jmssp.2010.193.204

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Keywords

  • Numerical methods
  • numerical integration
  • quadrature
  • Newton-cotes
  • higher-order
  • analysis of error