In this study we develop a novel approach for improvement of the precision of numerical integration by using equal tangent slopes in order to partition the integration interval. As a result, two new composite numerical integration formulas are derived. Using continuous function properties, it is possible to analyze the error and convergence of these formulas. A practical example confirms the effectiveness of this method in improving the accuracy of numerical integration. Additionally, the paper delves into the convergence properties and the error reduction capabilities of the new formulas compared to the traditional trapezoidal and Simpson’s rules. The limitations of the developed approach are briefly discussed.
- Open Access
- Article
Equal Tangent Length Partitioning for High-Precision Numerical Integration
Author Information
Received: 18 Nov 2025 | Revised: 15 Jan 2026 | Accepted: 17 Mar 2026 | Published: 02 Apr 2026
Abstract
Keywords
References
- 1.
Mamatha, M.; Venkatesh, B.; Kumar, P.S.; et al. Numerical integration of some arbitrary functions over an ellipsoid using Gaussian quadrature rules. Int. J. Chem. Eng. 2024, 2024, 5321249.
- 2.
Zecevic, M.; Lebensohn, R.A. Approximation of periodic green’s operator in real space using numerical integration and its use in fast fourier transform-based micromechanical models. Int. J. Numer. Methods Eng. 2021, 122, 7536–7552.
- 3.
Jakub Prüher; Karvonen, T.; Oates, C.J.; et al. Improved calibration of numerical integration error in sigma-point filters. IEEE Trans. Autom. Control 2021, 66, 1286–1292.
- 4.
Banica, V.; Maierhofer, G.; Schratz, K. Numerical integration of schrdinger maps via the hasimoto transform. SIAM J. Numer. Anal. 2024, 62, 322–352.
- 5.
Yáñez, D.F. Numerical integration rules based on B-spline bases. Appl. Math. Lett. 2024, 156, 109142.
- 6.
Xia, Y.; Wan, Y.; Su, G.; et al. An improved numerical integration method for prediction of milling stability using the lagrange-simpson interpolation scheme. Int. J. Adv. Manuf. Technol. 2022, 120, 8105–8115.
- 7.
Moheuddin, M.M.; Uddin, M.J.; Kowsher, M. A new study to find out the best computational method for solving the nonlinear equation. Appl. Math. Sci. Int. J. 2019, 6, 15–31.
- 8.
Maure, O.P.; Mungkasi, S. Application of numerical integration in solving a reverse osmosis model. AIP Conf. Proc. 2019, 2202, 020043.
- 9.
Altwallbah, N.M.M.; Radzi, M.A.M.; Azis, N.; et al. New perturb and observe algorithm based on trapezoidal rule: Uniform and partial shading conditions. Energy Convers. Manag. 2022, 264, 115738.
- 10.
Georgiev, S.G.; Erhan, N.M. The taylor series method and trapezoidal rule on time scales. Appl. Math. Comput. 2020, 378, 125200.
- 11.
Zhu, C.; Li, C. Numerical Approximation and Computational Geometry, 1st ed.; Higher Education Press: Beijing, China, 2020; pp. 171–206.
How to Cite
Shi, J.; Song, W.; Sun, M. Equal Tangent Length Partitioning for High-Precision Numerical Integration. Nonlinear Analysis and Computer Simulations 2026, 1 (2), 6. https://doi.org/10.53941/nacs.2026.100006.
RIS
BibTex
Copyright & License
Copyright (c) 2026 by the authors.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Contents
References
Suite 4002 Level 4, 447 Collins Street, Melbourne, Victoria 3000, Australia
General Inquiries: info@sciltp.com