A Fourth-Order Parametric Iterative Approach for Solving Systems of Nonlinear Equations

In this paper, we present a novel one-parameter family with fourth-order convergence to solve nonlinear systems, along with its convergence analysis. Several numerical experiments including a Bratu problem, a mixed Hammerstein integral equation, and nonlinear optimization problems (namely, the Broyden banded function and the Broyden tridiagonal function) as well as applications of differential equations, are analyzed using the proposed schemes to demonstrate their effectiveness. The results indicate that these methods produce more accurate approximations and exhibit greater efficiency compared to existing approaches.