Vieta-Fibonacci Wavelet-Based Numerical Solutions for Population Growth Models

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, D.A.V. PG College, Siwan, J.P.U., Chapra, India.

2 Department of Mathematics, College of Science, Sultan Qaboos University, P. O. Box 36, Al-Khod 123, Muscat, Sultanate of Oman.

3 Department of mathematics, Baba Saheb Bhimrao Ambedkar University Lucknow, India.

4 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.

10.22034/cmde.2025.67333.3199

Abstract

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-
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
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
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
of the proposed technique, establishing VFWM as a powerful and efficient tool for the numerical study of biological systems.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 01 January 2026

Files

History

  • Receive Date: 15 May 2025
  • Revise Date: 22 December 2025
  • Accept Date: 31 December 2025

Share

How to cite

Statistics