Various Error Estimations for Several Newton–Cotes Quadrature Formulae in Terms of at Most First Derivative and Applications in Numerical Integration

Authors

  • M. W. Alomari
  • S. S. Dragomir

Keywords:

Newton–Cotes formulae, Numerical integration, Ostrowski’s inequality.

Abstract

Error estimates for midpoint, trapezoid, Simpson’s, Maclaurin’s, 3/8-Simpson’s and Boole’s type rules are obtained. Some related inequalities of Ostrowski’s type are pointed out. These results are obtained for mappings of bounded variation, Lipschitzian, and absolutely continuous mappings whose first derivatives are belong to Lp[a,b] (1≤p≤∞) Applications to numerical integration are provided.

Key words and phrases. Newton–Cotes formulae, Numerical integration, Ostrowski’s inequality.

2000 Mathematics Subject Classification. 26D15, 26D20, 41A55

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Published

2025-05-18

How to Cite

M. W. Alomari, & S. S. Dragomir. (2025). Various Error Estimations for Several Newton–Cotes Quadrature Formulae in Terms of at Most First Derivative and Applications in Numerical Integration. Jordan Journal of Mathematics and Statistics, 7(2), 89–108. Retrieved from https://jjms.yu.edu.jo/index.php/jjms/article/view/1084

Issue

Vol. 7 No. 2 (2014)

Section

Articles