A Computational Study of Numerical Integration in Physics Applications Using Trapezoidal and Simpson's Methods

Authors

  • Muhamad Agung Suhendra Department of Physics, Faculty of Science, Universitas Mandiri, Subang Indonesia
  • Sufiyah Assegaf Department of Physics, International Women University, Bandung Indonesia
  • Iqbal Robiyana Department of Physics, Faculty of Science, Universitas Mandiri, Subang Indonesia
  • Nurizati Department of Physics, Faculty of Science, Universitas Mandiri, Subang Indonesia

Keywords:

Numerical Integration, Trapezodia Rule, Simpson's Rule, Physics Applications, Efficiency Analysis

Abstract

This research conducts a comprehensive evaluation of the efficiency and accuracy of two widely-used numerical integration methods, the Trapezoidal Rule and Simpson's Rule, within the context of solving physics-related problems. The study focuses on four representative cases: the calculation of kinetic energy, the determination of electric field strength, the work done by an ideal gas, and the gravitational potential energy. The performance of these methods is analyzed through key metrics such as convergence behavior, error magnitude, and computational time. The findings reveal that Simpson's Rule consistently delivers higher accuracy compared to the Trapezoidal Rule, especially for functions exhibiting non-linear characteristics. This highlights Simpson's Rule as a preferred method for complex physical problems, while the Trapezoidal Rule remains effective for simpler cases requiring lower computational overhead.

References

A. F Abdulhameed and Q A Memon 2021 J. Phys.: Conf. Ser. 2090 012104. doi : 10.1088/1742-6596/2090/1/012104.

Hüseyin Budak, Fatih Hezenci, Hasan Kara, & Mehmet Zeki Sarikaya. (2023). Bounds for the Error in Approximating a Fractional Integral by Simpson’s Rule. Mathematics, 11(10), 2282. https://doi.org/10.3390/math11102282

U. K. Qureshi, A. A. Shaikhi, F. K. Shaikh, S. K. Hazarewal, & T. A. Laghari. (2021). New Simpson type method for solving nonlinear equations. Open Journal of Mathematical Sciences, 5(1), 94. https://doi.org/10.30538/oms2021.0148

Hasanain J. Kareem, Mohammed A. Abdulwahid, & Hasril Hasini. (2023). Experimental investigation of holdup fraction using the trapezoidal rule, Simpson’s rule and the average offset formula in perforated horizontal wellbore. Results in Engineering, Vol 18, Iss , Pp 101131-. https://doi.org/10.1016/j.rineng.2023.101131

Waluyo, W., Kania, S., & HAMLAR, F. (2020). Comparative Computations on Supplied and Lost Energy utilizing Numerical Integrations. http://eprints.itenas.ac.id/2082/

Kong, Q., Siauw, T., & Bayen, A. (2020). Python Programming and Numerical Methods: A Guide for Engineers and Scientists (1st ed.). Elsevier. ISBN: 9780128195499.

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Published

2024-09-30

How to Cite

Suhendra, M. A., Assegaf, S., Robiyana, I., & Nurizati. (2024). A Computational Study of Numerical Integration in Physics Applications Using Trapezoidal and Simpson’s Methods. TIME in Physics, 2(2), 85–95. Retrieved from https://ejournal.universitasmandiri.ac.id/index.php/timeinphys/article/view/145

Issue

Vol. 2 No. 2 (2024): September

Section

Articles

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Copyright (c) 2024 Muhamad Agung Suhendra, Sufiyah Assegaf, Iqbal Robiyana, Nurizati Robiyana

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This work is licensed under a Creative Commons Attribution 4.0 International License.