A COMPARATIVE STUDY ON THE CONVERGENCE AND ACCURACY OF NUMERICAL INTEGRATION METHODS
DOI:
https://doi.org/10.5281/zenodo.17447678Keywords:
Numerical Integration, Quadrature, Simpson’s Rule, Trapezoidal Rule, Error Analysis, Rate of Convergence, Numerical Methods.Abstract
This study investigates the accuracy of three fundamental numerical integration methods: the Rectangle Rule,Trapezoidal Rule, and Simpson’s Rule. We approximate the defnite integral of a smooth function, f (x) = sin(x) + 1, over
a fxed interval. By analyzing the absolute error as the number of subintervals increases, we empirically demonstrate
the methods’ rates of convergence. The results clearly show that Simpson’s Rule, with its higher-order O(h) accuracy,
converges signifcantly faster than the O(h²) accuracy of the other two methods.
References
Richard L. Burden, J. Douglas Faires, and Annette M. Burden. Numerical Analysis, 10th ed. Cengage Learning, 2015.
James Stewart. Calculus: Early Transcendentals, 8th ed. Cengage Learning, 2015.
Ward Cheney and David Kincaid. Numerical Mathematics and Computing, 7th ed. Cen- gage Learning, 2012.
Philip J. Davis and Philip Rabinowitz. Methods of Numerical Integration, 2nd ed. Aca- demic Press, 1984.
Kendall E. Atkinson. An Introduction to Numerical Analysis, 2nd ed. John Wiley & Sons, 1989.
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Published
2025-08-01
How to Cite
Jumaboyev Asadbek Shokirjon ugli. (2025). A COMPARATIVE STUDY ON THE CONVERGENCE AND ACCURACY OF NUMERICAL INTEGRATION METHODS. Innovation Science and Technology, 1(8), 31–33. https://doi.org/10.5281/zenodo.17447678
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