Nüfus artışının tahminlenmesi: Yeni bir bakış açısı

Abstract

Bu makalede, araştırmacılar büyüme denklemini spline enterpolasyonu yoluyla değiştirerek nüfus artışını tahmin etmek için yeni bir yöntem geliştirmiş ve bunu 1935'ten 2025'e kadar olan dönemi kapsayan TSI verilerini kullanarak test etmişlerdir. Bu makale, kesikli verilerden sürekli verilere geçişin bir uygulamasını içermesi açısından önemlidir. Son olarak, diferansiyel denklemi çözmek için doğrusal spline enterpolasyonu kullanılmış ve elde edilen bulgular Mesterton-Gibbons yöntemiyle elde edilenlerle karşılaştırılmıştır.

Keywords

• Büyüme denklemi
• lojistik büyüme modeli
• nüfus artışı
• spline enterpolasyonu

Estimating Population Growth: A Novel Perspective

Abstract

In this paper, by modifying the growth equation via spline interpolation, the researchers developed a new method to estimate population growth and tested it using TSI data covering the period from 1935 to 2025. This paper is significant for including an application of the transition from discrete to continuous data. Finally, linear spline interpolation was used to solve the differential equation, and the resulting findings were compared with those obtained using Mesterton-Gibbons’ method.

Keywords

• growth equation
• logistic growth model
• population growth
• spline interpolation

References

1. [1] S. L. Manu and S. Shikaa, “Mathematical modeling of Taraba State population growth using exponential and logistic models,” Results in Control and Optimization, vol. 12, p. 100265, Sep. 2023, doi: 10.1016/j.rico.2023.100265.
2. [2] J. Shen and N. Spence, “Modelling regional population growth in China,” Math. Popul. Stud., vol. 6, no. 3, pp. 241–274, Mar. 1997, doi: 10.1080/08898489709525434.
3. [3] T. Brechet and S. Lambrecht, “Family altruism with renewable resource and population growth,” Math. Popul. Stud., vol. 16, no. 1, pp. 60–78, Jan. 2009, doi: 10.1080/08898480802619645.
4. [4] R. M. Sibly and J. Hone, “Population growth rate and its determinants: an overview,” Philos. Trans. R. Soc. Lond. B Biol. Sci., vol. 357, no. 1425, pp. 1153–1170, Sep. 2002, doi: 10.1098/rstb.2002.1117.
5. [5] D. Irk and M. A. Mersin, “Cubic b-spline quasi-interpolation method for regularized long wave equation,” Journal of Engineering Technology and Applied Sciences, vol. 3, no. 3, pp. 173–187, Dec. 2018, doi: 10.30931/jetas.448622.
6. [6] M. Zorşahin Görgülü, “A new algorithm based on the decic (tenth degree) b-spline functions for numerical solution of the equal width equation,” Journal of Engineering Technology and Applied Sciences, vol. 7, no. 3, pp. 185–194, Dec. 2022, doi: 10.30931/jetas.1072151.
7. [7] İ. Arsel et al., “A new approach to estimating solar radiation,” International Journal of Renewable Energy Research, vol. 14, no. 3, pp. 450–457, 2024.
8. [8] Ö. Özmen, “Fisher’s denkleminin kuintik B-splıne fonksiyonları yardımı ile çözülmesi,” Master’s Thesis, Aksaray University, Aksaray, 2013.

9. [9] A. Genç, İ. Kinaci, G. Oturanç, A. Kurnaz, Ş. Bilir, and N. Özbalta, “Statistical analysis of solar radiation data using cubic spline functions,” Energy Sources, vol. 24, no. 12, pp. 1131–1138, Dec. 2002, doi: 10.1080/00908310290087058.
10. [10] M. Mesterton-Gibbons, “A model of U.S. population growth,” in A Concrete Approach to Mathematical Modelling, Reading, MA: Addison-Wesley, 1989, ch. 1.9, pp. 26–29.
11. [11] F. Yılmaz, “Weibull dağılımına uyum iyiliği testlerinde parametre tahminlerinin etkisi,” Master’s Thesis, Necmettin Erbakan University, Konya, 2024.
12. [12] D. Hathout, “Modeling population growth: Exponential and hyperbolic modeling,” Appl. Math. (Irvine)., vol. 04, no. 02, pp. 299–304, 2013, doi: 10.4236/am.2013.42045.
13. [13] A. L. Jensen, “Comparison of logistic equations for population growth,” Biometrics, vol. 31, no. 4, p. 853, Dec. 1975, doi: 10.2307/2529810.
14. [14] M. J. Coleman, “Population modeling with ordinary differential equations,” 2006.
15. [15] C. De Boor, A practical guide to splines, Rev. Ed., vol. 27. Springer, 2001.
16. [16] R. L. Burden and J. D. Faires, Numerical analysis, 9th ed. Boston: Cengage Learning, 2010.
17. [17] TSI, “Nüfus istatistikleri portalı.” Accessed: Oct. 19, 2025. [Online]. Available: https://nip.tuik.gov.tr/
18. [18] Maplesoft, “Maple,” 2007, Waterloo Maple Inc: 11. Accessed: Oct. 19, 2025. [Online]. Available: https://www.maplesoft.com
19. [19] IBM Corp, “IBM SPSS Statistics for Windows,” 2015, IBM Corp: 23.