<p>In numerous real-world applications within applied sciences and engineering, nonlinear equations frequently arise and require effective numerical methods to obtain approximate solutions. The field of computational science is continually advancing, marked by the development of new iterative algorithms and enhancements to existing ones. Although some of these numerical methods may involve higher computational costs, they often achieve faster convergence rates, thereby improving overall efficiency in solving complex problems. In this paper, we propose a new parameterized iterative scheme for solving nonlinear equations. The method achieves fourth-order convergence by integrating Jarratt’s perturbed Newton method with a specially designed iterative function. This function utilizes a rational approximation of degree two in both its numerator and denominator, enhancing the method’s efficiency in solving nonlinear equations. The design allows for adaptability through parameter variations, enabling the method to be tailored for various nonlinear models. The iterative process is enhanced by an auxiliary term and a correction factor that improves convergence behavior. We analyze the convergence of the proposed scheme under certain assumptions and provide a detailed study of its basin of attraction. The basins of attraction for various initial guesses are explored to demonstrate the efficiency and robustness of the method. Furthermore, we establish that the scheme achieves optimal convergence order as per the Kung-Traub conjecture, making it a powerful method for solving nonlinear equations. Numerical experiments confirm the theoretical results and illustrate the superiority of the proposed method over existing techniques.</p>