Simpson’s 38 Methods to Calculate Approximate Area of West Java Province

Arya Ashari; Tasmi Tasmi; Geovanni Rikal Bunga; Dwi Catur Cahyaningsih; Muhammad Almuzakki

doi:10.25299/itjrd.2026.25717

Authors

Arya Ashari Department of Computer Science, Universitas Pertamina
Tasmi Tasmi Department of Computer Science, Universitas Pertamina
Rikal Department of Computer Science, Universitas Pertamina
Catur Department of Computer Science, Universitas Pertamina
Zaki Department of Computer Science, Universitas Pertamina

DOI:

https://doi.org/10.25299/itjrd.2026.25717

Keywords:

Numerical Integration, Simpson’s 3/8 Rule, Newton-Cotes Formulas, Area Approximation, Error Analysis

Abstract

Numerical methods represent an indispensable mathematical technique employed to address complex problems that cannot be resolved through analytical means. This study concentrates on the utilisation of Newton-Cotes numerical integration techniques, specifically Simpson's 3/8 rule, to provide an accurate estimation of the area of West Java Province, Indonesia. Previous research has employed the trapezoidal rule to approximate this area, resulting in an estimated error rate of 3.51%. In contrast, this investigation employs Simpson's 3/8 method, which utilises cubic polynomial interpolationover subintervals to provide more precise area calculations. The study demonstrates that increasing the number of partitions (9, 18, and 36) leads to progressively improved accuracy when the province is divided into quadrants. The findings demonstrate that Simpson's 3/8 rule consistently outperforms the trapezoidal method in estimating the area, achieving a minimum error of 2.97% with 36 partitions. This research not only validates the effectiveness of Simpson's 3/8 method for area approximation but also establishes a foundation for future studies aimed at enhancing numerical integration techniques in geographic analysis.

Downloads

Download data is not yet available.

References

[1] Aayushi Sahgal, “Implementation of Numerical Methods for Solving Differential Equations using Python,” International Journal for Research Publication and Seminar, vol. 14, no. 4, pp. 133–140, sep 2023, https://doi.org/10.36676/jrps.2023-v14i4-019.

[2] U. Khalid Qureshi, “Implementation of Numerical Integration Simpson 3/8 Rule to Develop aNumerical Simpson Iterative Method for Solving Non-Linear Equations,” Punjab University Journal of Mathematics, pp. 659–664, oct 2022, https://doi.org/10.52280/pujm.2022.541003.

[3] M. Mulyono, “Evaluasi dari metode: trapesium, simpson 1/3, simpson 3/8 dan newton cotes orde 4-10 untuk menghitung integral tertentu secara numerik,” AKSIOMA : Jurnal Matematika dan Pendidikan Matematika, vol. 13, no. 3, pp. 466–479, dec 2022,

https://doi.org/10.26877/aks.v13i3.12908.

[4] M. J. Uddin, Mir Md. Moheuddin, and Md. Kowsher, “A New Study of Trapezoidal, Simpson’s 1/3 and Simpson’s 3/8 Rules of Numerical Integral Problems,” Applied Mathematics and Sciences An International Journal (MathSJ), vol. 6, no. 4, pp. 01–13, dec 2019,

https://doi.org/10.5121/mathsj.2019.6401.

[5] M. M. Moheuddin, M. A. S. Titu, and S. Hossain, “A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods,” Pure and Applied Mathematics Journal, vol. 9, no. 3, pp. 46–54, 2020, https://doi.org/10.11648/j.pamj.20200903.11.

[6] W. Guo, “Solving problems involving numerical integration (): Modified Simpson’s methods for equal intervals of odd numbers,” STEM Education, vol. 3, no. 3, pp. 171–189, 2023, https://doi.org/10.3934/steme.2023011.

[7] Z. A. Khudhair, “Innovative Acceleration Methods to Numerically Optimize the Values of Integrals with Simpson Rule 3/8,” International Academic Journal of Science and Engineering, vol. 11, no. 1, pp. 165–168, jan 2024, https://doi.org/10.71086/IAJSE/V11I1/IAJSE1119.

[8] H. Budak, F. Hezenci, H. Kara, and M. Z. Sarikaya, “Bounds for the Error in Approximating a Fractional Integral by Simpson’s Rule,” Mathematics, vol. 11, no. 10, 2023, https://doi.org/10.3390/math11102282.

[9] M. Rostamian Delavar, A. Kashuri, and M. De La Sen, “On Weighted Simpson’s 38 Rule,” Symmetry, vol. 13, no. 10, 2021, https://doi.org/10.3390/sym13101933.

[10] P. Yafet, “Penerapan Integral Numerik Dalam Menghitung Luas Daerah Tidak Beraturan,” Asimtot : Jurnal Kependidikan Matematika, vol. 1, no. 2 SE - Articles, pp. 127–132, https://doi.org/10.30822/asimtot.v1i2.278.

[11] A. Isaac, T. Boakye Stephen, and B. Seidu, “A New Trapezoidal-Simpson 3/8 Method for Solving Systems of Nonlinear Equations,” American Journal of Mathematical and Computer Modelling, vol. 6, no. 1, p. 1, 2021, https://doi.org/10.11648/j.ajmcm.20210601.11.

[12] X. Du, P. Ren, and J. Zheng, “Predicting Milling Stability Based on Composite Cotes-Based and Simpson’s 3/8-Based Methods,” Micromachines, vol. 13, no. 5, p. 810, may 2022, https://doi.org/10.3390/mi13050810.

[13] A. Vulovi´c and N. Filipovic, “Application of numerical methods for the analysis of respiratory system,” in Cardiovascular and Respiratory Bioengineering. Elsevier, 2022, pp. 225–235, https://doi.org/10.1016/B978-0-12-823956-8.00005-5. [Online]. Available:

https://linkinghub.elsevier.com/retrieve/pii/B9780128239568000055

[14] W. N. Fauziyah, “Numerical Integration Implementation Using Trapezoidal Rule Method To Calculate Aproximation Area Of West Java Province,” International Journal of Quantitative Research and Modeling, vol. 2, no. 2, pp. 117–124, jun 2021,

https://doi.org/10.46336/ijqrm.v2i2.136.

[15] A. J. Ali and A. F. Abbas, “Applications of Numerical Integrations on the Trapezoidal and Simpson’s Methods to Analytical and MATLAB Solutions,” Mathematical Modelling of Engineering Problems, vol. 9, no. 5, pp. 1352–1358, dec 2022,

https://doi.org/10.18280/mmep.090525.

[16] S. Rahayu and A. Hindasyah, “Comparative Analysis of Numerical Integration Solutions Pias Method and Newton Cotes Method Using Python Programming Language,” Mathline : Jurnal Matematika dan Pendidikan Matematika, vol. 8, pp. 1321–1332, 2023,

https://doi.org/10.31943/mathline.v8i4.492.

[17] M. Engler, “Fast Numerical Simpson and Boole Integration by Using the Derivatives at the Boundaries,” aug 2023, https://doi.org/10.21203/rs.3.rs-3277963/v1.

[18] S. C. Chapra and R. P. Canale, Numerical methods for engineers, 6th ed. Boston: McGraw-Hill Higher Education, 2010.

[19] J. H. Mathews, “Simpson’s 3/8 Rule for Numerical Integration,” 2004. [Online]. Available: https://web.archive.org/web/20081204012519/http://math.fullerton.edu/mathews/n2003/Simps

on38RuleMod.html

[20] Badan Pusat Statistik Provinsi Jawa Barat, “Luas Daerah (km²),” 2022. [Online]. Available: https://jabar.bps.go.id/id/statistics-table/2/MjQ0IzI=/luas-daerah.html