On Extending the Applicability of Iterative Methods for Solving Systems of Nonlinear Equations

In this paper, we present a technique that improves the applicability of the result obtained by Cordero et al. in 2024 for solving nonlinear equations. Cordero et al. assumed the involved operator to be differentiable at least five times to extend a two-step p-order method to order $p+3$. We obtained the convergence order of Cordero et al.’s method by assuming only up to the third-order derivative of the operator. Our analysis is in a more general commutative Banach algebra setting and provides a radius of the convergence ball. Finally, we validate our theoretical findings with several numerical examples. Also, the concept of basin of attraction is discussed with examples.