An optimal eighth order Ostrowski's - based iterative scheme for nonlinear systems arising in biological and neuroscience models

Abstract

This paper presents an optimal eighth order multi-step iterative method based on Ostrowski’s fourth-order approach, designed for solving nonlinear equations and systems with high efficiency and accelerated convergence. The method requires only three function evaluations and one derivative evaluation per iteration, achieving high precision while reducing computational costs. It satisfies the Kung–Traub optimality conjecture for n-4, ensuring theoretically optimal convergence. This method is particularly suitable for applications in mathematical biology and neuroscience, such as modeling interacting with neuronal populations, gene regulatory networks, and multi-compartment physiological systems. Numerical examples demonstrate that the proposed approach provides fast, accurate, and reliable solutions, outperforming classical methods and offering a versatile tool for analyzing complex biological and neural systems.