University of Tabriz Computational Methods for Differential Equations 2345-3982 Articles in Press 2026 01 01 Vieta-Fibonacci Wavelet-Based Numerical Solutions for Population Growth Models 21046 10.22034/cmde.2025.67333.3199 EN Jay Kishore Sahani Department of Mathematics, D.A.V. PG College, Siwan, J.P.U., Chapra, India. Nikhil Khanna Department of Mathematics, College of Science, Sultan Qaboos University, P. O. Box 36, Al-Khod 123, Muscat, Sultanate of Oman. Gopal Datt Department of mathematics, Baba Saheb Bhimrao Ambedkar University Lucknow, India. Dumitru Baleanu 1. Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Ankara TR-06530, Turkey.\\ 2. Institute of Space Science, Magurle, Bucharest R-077125, Romania. Journal Article 2025 05 15 In this article, we introduce a novel numerical approach for solving biological population growth models using the Vieta-Fibonacci wavelet-based collocation method (VFWM). The proposed scheme trans-<br />forms the governing nonlinear differential equations into a system of algebraic equations by employing the truncated Vieta-Fibonacci wavelet, which is then solved via the Newton-Raphson method. To the best of<br />our knowledge, we also apply the Haar wavelet method (HWM) to these models for the first time, providing a new benchmark for comparison. A comprehensive set of numerical experiments on diverse population<br />growth models demonstrate the robustness of VFWM in handling nonlinear dynamics. The results show that VFWM consistently outperforms HWM and other existing numerical schemes, such as the Runge-Kutta-Fehlberg method and the Laplace Adomian Decomposition Method, both in terms of accuracy and computational efficiency. The convergence and error analysis further confirm the stability and reliability<br />of the proposed technique, establishing VFWM as a powerful and efficient tool for the numerical study of biological systems. https://cmde.tabrizu.ac.ir/article_21046_9fe148f2129aea0ced867ae96d47a109.pdf